A Framework for Supporting DBMS

A Framework for Supporting DBMS
A Framework for Supporting DBMS-like Indexes
in the Cloud
Gang Chen
Hoang Tam Vo, Sai Wu, Beng Chin Ooi
National University of Singapore
University of Waterloo
[email protected]
{voht, wusai, ooibc}@comp.nus.edu.sg
[email protected]
Zhejiang University
ABSTRACT
To support “Database as a service” (DaaS) in the cloud, the database
system is expected to provide similar functionalities as in centralized DBMS such as efficient processing of ad hoc queries. The
system must therefore support DBMS-like indexes, possibly a few
indexes for each table to provide fast location of data distributed
over the network. In such a distributed environment, the indexes
have to be distributed over the network to achieve scalability and reliability. Each cluster node maintains a subset of the index data. As
in conventional DBMS, indexes incur maintenance overhead and
the problem is more complex in the distributed environment since
the data are typically partitioned and distributed based on a subset
of attributes. Further, the distribution of indexes is not straight forward, and there is therefore always the question of scalability, in
terms of data volume, network size, and number of indexes.
In this paper, we examine the problem of providing DBMS-like
indexing mechanisms in cloud DaaS, and propose an extensible,
but simple and efficient indexing framework that enables users to
define their own indexes without knowing the structure of the underlying network. It is also designed to ensure the efficiency of
hopping between cluster nodes during index traversal, and reduce
the maintenance cost of indexes. We implement three common
indexes, namely distributed hash indexes, distributed B+ -tree-like
indexes and distributed multi-dimensional indexes, to demonstrate
the usability and effectiveness of the framework. We conduct experiments on Amazon EC2 and an in-house cluster to verify the
efficiency and scalability of the framework.
1.
INTRODUCTION
The cloud simplifies the deployment of large-scale applications
by shielding users from the underlying infrastructure and implementation details. There is substantial interest in cloud deployment of data-centric applications. One good example application
is the Customer Relationship Management (CRM), which is used
to monitor sales activities, and improve sales and customer relationships. While there are daily account maintenance and sales activities, there are certain periods when sales quota must be met,
forecasting and analysis are required, etc., and these activities rePermission to make digital or hard copies of all or part of this work for
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their results at The 37th International Conference on Very Large Data Bases,
August 29th - September 3rd 2011, Seattle, Washington.
Proceedings of the VLDB Endowment, Vol. 4, No. 11
Copyright 2011 VLDB Endowment 2150-8097/11/08... $ 10.00.
M. Tamer Özsu
quire more resources at peak periods, and the cloud is able to meet
such inconsistent resource requirements.
To support data-centric applications, the cloud must provide an
efficient and elastic database service with database functionality,
which is commonly referred to as the “database as a service” (DaaS).
This work is part of our cloud-based data management system,
named epiC (elastic power-aware data-intensive Cloud)1 , which is
designed to support both analytical and OLTP workloads. In this
paper we focus on the provision of indexing functionality in the
context of DaaS. One obvious requirement for this functionality is
to locate some specific records among millions of distributed candidates in real time, preferably within a few milliseconds. A second requirement is to support multiple indexes over the data – a
common service in any DBMS. Another important requirement is
extensibility by which users can define new indexes without knowing the structure of the underlying network or having to tune the
system performance by themselves.
Currently no DaaS satisfies these requirements. Most popular
cloud storage systems are key-value based, which, given a key, can
efficiently locate the value assigned to the key. Examples of these
are Dynamo [5] and Cassandra [8]. These systems build a hash
index over the underlying storage layer, partitioning the data by
keys (e.g., primary index). For supporting primary range index, a
distributed B-tree has been proposed [2]. While these proposals
are efficient in retrieving data based on primary index, they are not
useful when a query does not use the key as the search condition.
In these cases, sequential (or even parallel) scanning of an entire
(large) table is required to retrieve only a few records, and this is
obviously inefficient.
Recently, Cassandra [8] has started to support native distributed
indexes on non-key attributes. However, these secondary indexes
are restricted to hash indexes. A second line of research has been
view materialization in the cloud to support ad hoc queries. In [1], a
view selection strategy was proposed to achieve a balance between
query performance and view maintenance cost. Secondary indexes
can be implemented as a specific type of materialized views. Maintaining materialized views is orthogonal to our research and the
comparison with this approach is our on going research.
Two secondary indexes have been proposed for cloud systems: a
distributed B+ -tree-like index to support single-dimensional range
queries [22], and a distributed R-tree-like index to support multidimensional range and kNN (k Nearest Neighbor) queries [21]. The
main idea of both indexes is to use P2P routing overlays as global
indexes and combine with local disk-resident indexes at each index
node. The overlays are used to build a logical network for partitioning data, routing queries and distributing the system workload. In
contrast, IR based strategies in integrating distributed independent
1
http://www.comp.nus.edu.sg/∼epiC
databases over unstructured network, without any global index, are
proposed in [13].
Like Dynamo [5] and Cassandra [8], our system adopts the peerto-peer (P2P) model to provide highly available service with no
single point of failure. Moreover, using DHT overlays as infrastructure also allows building an elastic indexing service where index nodes can be added or reduced based on load characteristics. In
addition, while the proposals in [21, 22] illustrate the feasibility of
supporting an index using the underlying overlay network, it is not
feasible to support multiple indexes using these approaches since it
is expensive to maintain multiple overlays – each overlay for a specific index – over the distributed cluster nodes. In order to provide
an indexing functionality that is able to support a variety of basic
indexes efficiently, we propose an extensible indexing framework
that supports multiple indexes over a single generic overlay.
Our framework is motivated by the observation that many P2P
overlays are instances of the Cayley graph [12, 14]. Consequently,
we abstract the overlay construction by a set of Cayley graph interfaces. By defining the customized Cayley graph instances, a user
can create different types of overlays and support various types of
secondary indexes. This approach avoids the overhead of maintaining multiple overlays, as discussed above, while maintaining flexibility, and it achieves the much needed scalability and efficiency
for supporting multiple indexes of different types in cloud database
systems.
The main challenge in developing this framework is how to map
different types of indexes to the Cayley graph instances. To address
this problem, we define two mapping functions, a data mapping
function and an overlay mapping function. The data mapping function maps various types of values into a single Cayley graph key
space. We propose two data mapping functions: a uniform mapping function, which assumes the data are uniformly distributed
and maps data to different keys with the same probability, and a
sampling-based mapping function, which maps data based on the
distribution of samples. The overlay mapping function is composed
of a set of operators that represent the routing algorithms of different Cayley graph instances. The user can define new types of
overlays by implementing new operators, which simplifies the inclusion and deployment of new types of indexes. Additionally, the
use of data mapping and overlay mapping reduces the cost of index
creation and maintenance.
Performance tuning in a cloud system is not trivial, and therefore,
our indexing framework is designed to be self tunable. Independent of the index type, our self tuning strategies optimize the performance by adaptively creating network connections, effectively
buffering local indexes and aggressively reducing the random I/Os.
In summary, the contributions of the paper are as follows.
• We propose an extensible framework for implementing DBMSlike indexes in the cloud. We exploit the characteristics of
Cayley graphs to provide the much needed scalability for
supporting multiple distributed indexes of different types.
• We define a methodology to map various types of data and
P2P overlays to a generalized Cayley graph structure.
• We propose self-tuning strategies to optimize the performance
of the indexes defined over the generic Cayley overlay, thereby
achieving high performance and scalability.
• We implement the proposed framework and conduct extensive experimental study on Amazon EC2 and an in-house
cluster. The results confirm the robustness, efficiency and
scalability of our proposed framework.
The paper proceeds as follows. In Section 2, we give an overview
of the indexing framework. We present the Cayley graph based
indexing scheme in Section 3. We evaluate the performance of the
indexes in Section 4 and conclude the paper in Section 5.
2. OVERVIEW OF THE FRAMEWORK
The proposed framework consists of an indexing service that is
loosely connected with other cloud services, such as storage service and processing service. This is a commonly accepted design
principle in the cloud, which enables different services to scale up
and down independently. The indexing service runs as a set of distributed processes on the virtual machines. The indexing service
interacts with the underlying storage service where the base tables
are stored, e.g. distributed file systems (DFS), and provides data
retrieval interface for the upper layer applications.
We refer to the index process that runs on a virtual machine as
an index node. The index nodes are organized into a generic Cayley graph based overlay. Figure 1 shows the architecture of the
indexing service. The multiple types of indexes supported by the
Storage Service
e.g. DFS, K-V store
Index Node
Data Mapping
Cayley Graph Manager
query
index data
Index Node
Data Mapping
Cayley Graph Manager
Local Indexes
...
Virtual machine
Cayley
overlay
Index Node
Data Mapping
Local Indexes
...
Virtual machine
Cayley Graph Manager
Local Indexes
...
Virtual machine
Figure 1: Indexing service in the cloud
framework are mapped to Cayley graph instance managed by the
Cayley Graph Manager. One Cayley graph instance is required for
each type of index. For example, a hash index on a string or numeric attribute is mapped to a Chord [19] instance while a kd-tree
or R-tree index on multiple attributes can be supported by a CAN
[16] instance. Cayley graph is described further in Section 3.1. We
define a generalized key space S for the Cayley graph. A client
application simply needs to define a data mapping function F that
maps an index column c to a value in S. Based on the type of indexes, different F s can be defined. If the index is built to support
range index, F must preserve the locality of data. Otherwise, F
can be defined as a universal hash function to balance the system
load.
After being mapped with function F , the value of the index keys
are normalized to the Cayley graph key space. The detailed description of the data mapping technique is presented in Section 3.2.
The indexing process in our framework is similar to the publication
process in P2P overlays. Specifically, an index entry is composed
of a key-value pair (k, v), where k denotes the value of the index
column and v is the offset of the tuple in the underlying DFS or the
value of the tuple itself (or possibly portions of the tuple) if the user
opts to use covering indexes. Under the covering index scheme, the
indexes include additional, non-key columns in the index entries
so that they can service the queries without having to refer to the
base records, i.e., the indexes “cover” the queries. To index this
key-value pair (k, v), we apply a P2P overlay routing protocol to
publish (k, v) based on k0 , the mapped value of k with the map-
ping function F . Upon receiving a key-value pair (k, v) and the
mapped key k0 from the data mapper, the Cayley graph manager
retrieves the corresponding instance of the index column and applies the routing protocols of the instance to index the data. Based
on the routing protocol of the Cayley graph instance, the index node
in the cluster system is responsible for a key set and needs to keep
a portion of index data (i.e., the published data).
A typical database application such as Human Resource Management or Customer Relationships Management has many tables,
and each table has a few indexes. Given the size of the current
datasets, the index data will be too large to be maintained in memory. To address this problem, each index node is expected to create
one local disk-resident index such as the hash table or B+ -tree for
maintaining the index data of a distributed index. Thus, the index
lookup is performed in two steps. In the first step, we follow the
routing protocol defined by the Cayley graph operators to locate the
node responsible for the index data. In the second step, we search
the node’s local index to get the index data. To further improve the
search performance, we employ a buffer manager locally to reduce
the I/O cost for traversing local indexes.
It is important to note that we aim to design a simple yet efficient
and scalable solution for indexing data in the cloud. Our indexing system is different from current proposals [21, 22] in two main
aspects. First, our indexing system provides the much needed scalability with the ability to support a large number of indexes of different types. Second, in our design the indexing system is loosely
coupled with the storage system while the indexes in [21, 22] ride
directly on the data nodes of the storage system. Decoupling system functions of a cloud system into loosely coupled components
enables each component to scale up and scale down independently.
3.
CAYLEY GRAPH-BASED INDEXING
In this section, we present a Cayley graph-based indexing scheme
and use it to support multiple types of distributed indexes, such as
hash, B+ -tree-like and multi-dimensional index, on the cloud platform.
3.1
Mapping P2P Overlays to Cayley Graph
Cayley graph, which encodes the structure of a discrete set, is
defined as follows.
L
D EFINITION 1. Cayley Graph : A Cayley graph GL= (S, G, ),
where S is an element set, G is a generator set and
is a binary
operator, is a graph such that
1. ∀e ∈ S, there is a vertex in G corresponding to e.
L
2.
: (S × G) → S.
L
3. ∀e ∈ S and ∀g ∈ G,
Le g is an element in S and there is
an edge from e to e g in G.
L
4. There is no loop in G, namely ∀e ∈ S, ∀g ∈ G → e g 6=
e.
In a Cayley graph, we create a vertex for each element L
in S. If for
elements ei and ej , there is a generator g satisfying ei
g = ej ,
then edge (ei → ej ) is created.
Each node in the Cayley graph can be considered a peer, allowing the Cayley graph to define a P2P overlay. Many P2P overlays,
including Chord [19], an expanded BATON [7], and CAN [16],
can be mapped to an instance of Cayley graph [12]. We discuss
how this mapping occurs.
When a cluster node assumes the role of an index node in the
Cayley graph, we use a hash function to generate a unique value in
S as its identifier. Suppose the list of index nodes is {n0 , n1 , ..., nd }
and let I(ni ) denote node ni ’s identifier. I(ni ) refers to an element
in S and an abstract vertex in the Cayley graph. To support index
construction, we partition the element set into subsets with continuous elements based on nodes’ identifiers. We first sort the nodes
by their identifiers and hence, I(ni ) < I(ni+1 ). The subset Si is
defined as
½
{x|I(ni−1 ) < x ≤ I(ni )}
if x 6= 0
Si =
{x|0 ≤ x ≤ I(ni ) ∨ I(nd ) < x ≤ S.max} otherwise
where S.max is the maximal element in S. Node ni is responsible
for subset Si . The overlay mapping problem is formalized as:
D EFINITION 2. Overlay Mapping
L : Given a P2P overlay O
and a Cayley graph G = (S, G, ), O can be mapped to G by
using the following rules:
1. For a node n in O, I(n) is defined as an element in S.
2. Given two nodes, ni and nj , nj is a routing neighbor
of ni ,
L
iff there is a generator g in G, satisfying I(ni ) g ∈ Sj .
In a Cayley graph, the element set and generator set can be defined arbitrarily, which makes the mapping problem very complex.
In our proposal, we fix the element set S and the generator set G as
{x|0 ≤ x ≤ 2m − 1} and {2i |0 ≤ i ≤ m − 1}, respectively. In
this way, L
the overlay mapping problem is transformed into finding
a proper
for each overlay. Popular P2P overlays such as Chord
[19], CAN [16] and BATON [7] can be easily integrated into the
above model. In fact, these three overlays are sufficient to support
DBMS-like indexes similar to those commonly available in commercial centralized DBMS, namely the hash, B+ -tree and R-tree.
In the following example, we show how to map Chord to the
Cayley graph by defining a proper operator. Details of mapping
other overlays are shown in Appendix A.
In our framework, Chord is a 2m -ring since Cayley graph’s element set is {x|0 ≤ x ≤ 2m − 1} (we set m = 30 in ourL
experiments to support large datasets). We define the operator x y
as (x + y) mod 2m . Therefore, given a node ni and its identifier I(ni ) in the element set S, we create edges between I(ni ) to
keys I(ni ) + 2k (0 ≤ k ≤ m − 1), based on the generator set
{2i |0 ≤ i ≤ m − 1}. Namely, each node maintains m routing entries, which follows the structure of Chord. Algorithm 1 shows the
routing algorithm that simulates the Chord protocol. In Algorithm
1, ni refers to the index node that receives the routing request and
start is the node’s identifier. Basically, we iterate all generators
and try to route the message as far as possible. In line 7, given a
key, the function getN odeByKey returns the address of the index
node that is responsible for the key based on the routing table.
Algorithm 1 ChordLookup(Node ni , Key dest)
1. Key start= I(ni )
2. if start == dest then
3.
return node
4. else
5.
for i=m-1 to 0 do
6.
if (start + 2i mod 2m ) ≤ dest then
7.
Node nextN ode = getN odeByKey(start + 2i )
8.
return nextN ode
3.2 Data Mapping
The indexed columns may have different value domains. Since
we use the values of indexed columns as the keys to build the index,
before publishing an index entry with key k we need to normalize
k into a value k0 in the element space S. For this purpose, some
key mapping functions are required. Given an element domain S
and an attribute domain D, the mapping function f : D → S maps
every value in D to a unique value in S.
Suppose we have d index nodes, {n0 , n1 , ..., nd }, and use Si to
denote the element subset of ni . Given a table T , if the index is
built for T ’s column c0 , the number of index entries published to
ni is estimated as:
X
g(ni ) =
Φ(f (tj .c0 ))
(1)
tj ∈T
where function Φ(x) returns 1 if x ∈ Si , or 0, otherwise.
A good mapping function should provide the properties of locality and load balance.
D EFINITION 3. Locality : The mapping function f : D → S
satisfies the locality property, if ∀xi ∀xj ∈ D ∧ xi < xj →
f (xi ) ≤ f (xj ).
D EFINITION 4. ²-Balance : The mapping function f : D → S
is an ²-balance function for column c0 , if for any two cluster nodes,
g(ni )
ni and nj , g(n
< ².
j)
Locality requirement is used to support range queries, but is
not necessary for the hash index. Load balance guarantees that
the workload is approximately uniformly distributed over the index nodes. Definitions 3 and 4 can be extended to support multidimensional (multi-column) indexes. For the d-dimensional case,
the mapping function is defined as f : D0 × ... × Dd → S,
while the locality is measured by the average value of L(xi , xj ) =
d(xi ,xj )
, where d(xi , xj ) returns the Euclidean distance be|f (xi )−f (xj )|
tween two multi-dimensional points, xi and xj .
D EFINITION 5. d-Locality : The mapping function f : D0 ×
...×Dd → S satisfies the locality property, if the average L(xi , xj )
is bounded by a function of d.
In our current implementations, we provide two data mapping
functions: a uniform mapping function and a sampling-based mapping function.
8
0110
0111
1101
6
1111
(7,8)
0100
0101
1100
1110
1001
1011
Q
4
0001
0011
2
0000
0010
1000
1010
0
0
3
6
9
12
Figure 2: Mapping Multi-Dimensional Data
In the multi-dimensional case, we partition the space in a kdtree style. The key space is partitioned into sub-spaces by different dimensions iteratively. In the xth partition, we partition each
sub-space evenly by the jth dimension, where j=x mod d. Suppose we have 2a sub-spaces before partitioning. The next iteration
will generate 2a+1 sub-spaces. The partitioning process terminates
when 2m partitions are created. Then, we assign each partition an
m-length binary string as its ID, recording its partitioning history.
The ID can be transformed back to a value in [0, 2m − 1], namely
the key space of the Cayley graph. Note that in uniform mapping,
sub-spaces have equal size. Suppose the Cayley graph key space is
[0, 24 − 1] and the data domains are x = [0, 12] and y = [0, 8],
respectively. Figure 2 shows how a 2-D space is partitioned. The
point [7, 8] is transformed into 1101. Linking the partitions with
adjacent IDs generates a multi-dimensional Z-Curve.
T HEOREM 2. Z-Curve mapping provides a mapping function
that has the properties of d-locality and 1-balance for uniform distributions.
P ROOF. Hilbert-curve has been proven to satisfy d-Locality using the metric properties of discrete space-filling curve [6]. The
same proof technique can be applied for Z-Curve. Although ZCurve performs a bit worse than Hilbert-Curve, it still preserves
the locality property. As we split the space into equal-size partitions, we also achieve the 1-balance property for uniform distribution.
3.2.2 Sampling-based Data Mapping
P ROOF. Equation 2 is a monotonic increasing function and scales
the
original domain to the new key space using the same factor,
2m
. Therefore, it satisfies the two properties.
u−l
If data distribution is skewed, the uniform mapping function cannot provide a balanced key assignment. Hence, some nodes may
need to maintain more index data than the others, which is undesirable. Consequently, we may need to use a load balancing scheme
to shuffle the data dynamically during query processing, which is
costly. In our framework, a sampling-based approach is used to
address this problem.
Before we map and partition the space, we first collect random
samples from the base tables to get a rough estimate of the data
distribution. Seshadri and Naughton [17] showed that stratified random sampling method can guarantee perfect load balancing without reducing the accuracy of the estimation. Specifically, the domain being sampled is partitioned into disjoint subsets and a specified number of samples is taken from each subset.
Based on the retrieved samples, we map the data to S in such a
way that each partition in S has approximately the same number
of samples. In the one dimensional case, the partitioning strategy is equivalent to building an equal-depth histogram. In the kdimensional case, we apply the kd-tree style partitioning. When
partitioning a space, we guarantee that the generated subspaces
have the same number of samples.
For a string value, the uniform mapping function is defined as a
hash function h, which maps the string to a value in S. If the index
needs to support range queries for strings, h is implemented as a
locality sensitive hashing [4].
T HEOREM 3. The sampling-based mapping keeps locality and
provides log2 N -balance (N is the total number of cluster nodes),
if the samples provide an accurate estimate of the overall data distribution.
3.2.1
Uniform Data Mapping
The uniform mapping function assumes that the data are uniformly distributed in the key space. In the one dimensional case,
given a key k in original key space [l, u], we map it to the new value
f (k) = min(2m − 1, b
(k − l)2m
c)
u−l
(2)
For example, suppose the original domain is [0, 10] and the key
space of Cayley graph is [0, 22 ], keys 6 and 8 will be mapped to
values 2 and 3, respectively.
T HEOREM 1. When the data distribution is uniform, Equation
2 provides a mapping function that has the properties of locality
and 1-balance.
P ROOF. Since the proof of locality is similar to the uniform
case, we do not discuss it. For any two cluster nodes, ni and nj ,
|Si |
< log2 N [19]. In our sampling-based mapping approach,
|Sj |
each sub-space has the same number of samples. When we distribute the sub-spaces in the cluster, node ni will get k sub-spaces,
where k is proportional to |Si |. Therefore, if the samples provide an
accurate estimation for the data distribution, sampling-based mapping approach has the property of log2 N -balance.
It is notable that bulk insertion from external data sources into
cloud databases is a common operation [18]. For example, in a
webshop application, the system needs to bulk insert the daily feed
of new items from partner vendors into its operational table. Sampling operations are typically done during this bulk insertion process [18]. Therefore, the statistics such as data domains and data
distribution could be estimated quite accurately. Note that these
statistics might become obsolete due to many skewed online updates after the bulk insertion, and the distribution of the index data
among index nodes will become unbalanced as a result. However,
when the level of load imbalance reaches a predefined threshold,
the system can activate a data migration process to redistribute the
index data and update the data mapping function correspondingly.
Moreover, besides the default uniform and sampling-based mapping functions, the user can define his own mapping function by
extending the interface of the framework. In this interface, the
abstract mapping function is defined. The user can overload the
function with his customized implementation. When a mapping
function is linked with an index, our indexing framework will automatically invoke it to transform the data for indexing and querying.
Query Mapping. The objective of distributed indexes is to facilitate fast retrieval of a subset of data without having to scan every
data node. The query optimizer of the client applications will decide if index scan or full table scan should be employed. For queries
that involve a small portion of data that fall within a small range,
a simple but efficient mapping solution is sufficient to handle such
a query pattern. A range query Q, in the one dimensional case,
is mapped into a single key range, while in the multi-dimensional
case, is transformed into multiple key ranges. For example, in
Figure 2, the query Q = {3.5 ≤ x ≤ 8.5, 3 ≤ y ≤ 5.5}
is transformed into four key ranges, [0011, 0011], [0101, 0101],
[1001, 1001] and [1100, 1100]. To retrieve the index for Q, we
need to search the four key ranges in the Cayley graph.
3.3
Index Functions
In this section, we describe three basic functions provided by
the indexing framework for client applications to build the indexes,
perform search on the indexes, and update data in the indexes.
3.3.1
Index Building
In our current framework, we have provided the operators for
Chord [19], BATON [7] and CAN [16], as those overlays are used
to build the common distributed hash, B+ -tree-like and R-tree-like
indexes. The Cayley graph manager considers each operator as a
class of overlays. In the initialization process of an index for column c, suppose its operator is op, the Cayley graph manager registers the index as an instance of op. In other words, each operator
can have multiple instances, referring to different indexes on the
same type of overlays. The Cayley graph manager also keeps the
information of table name, column name, value domain and data
mapping function, which it broadcasts to all index nodes to initialize them.
Following the initialization, the index is created for each incoming tuple. Algorithm 2 shows how the index is built for a tuple. First
the overlay instance of the index is obtained from the Cayley graph
manager, which is then used to map and publish the data. In line 6,
the lookup function is an abstraction of the underlying routing algorithms, which will be transformed into different implementations
of the overlay. In line 7, the getIndexData(t) function returns the
offset of tuple t in the underlying DFS or the value of tuple t itself
(or possibly portions of the tuple t) if the user opts to use covering
indexes. Algorithm 2 demonstrates the extensibility of our indexing framework. It hides all the implementation details, such as how
data are mapped and which routing algorithms are used, by providing a highly abstract interface for users.
Algorithm 2 Insert(Tuple t, CayleyManager M )
1. for every column ci of t do
2.
if M .isIndexed(ci ) then
3.
Instance I = M .getInstance(ci )
4.
MappingFunction F = M .getMappingFunction(ci )
5.
Key k = t.ci
6.
Node n=I.lookup(F (k))
7.
IndexData v = getIndexData(t)
8.
publish (k, v) to n
3.3.2 Index Search
Regardless of the underlying overlays, the Search method can
be abstracted as outlined in Algorithm 3. The inputs of Search are
a search key and the index column name. The column name is used
to identify the specific index and the corresponding overlay. The
query engine first asks the Cayley graph manager to get the overlay
instance for the column. Then, it invokes the lookup method of the
overlay, which will return the index node that is responsible for the
search key.
Algorithm
3
Search(Key k, CayleyManager M
Column ci )
1. Instance I = M .getInstance(ci )
2. MappingFunction F = M .getMappingFunction(ci )
3. Node n=I.lookup(F (k))
4. Array< IndexV alue > values = n.localSearch()
5. for i = 0 to values.size-1 do
6.
getIndexTuple(values[i])
In line 4, after receiving the request, the index node performs a
search on its local disk-resident indexes to retrieve the indexed data
of the key, denoted as as a set of index values. If the index being
used is a covering index, then the returned index values themselves
are the tuples in the query result set. Otherwise, the index values are
only the pointers to the base records, i.e. the offsets of the records
in the underlying DFS. In this case, the system needs to invoke the
interfaces of the underlying DFS to perform random accesses based
on these offsets.
Range search can be processed in a similar way, except that in
line 3, multiple index nodes could be returned. In this case, the
query should be processed by these nodes in parallel. We note
that this parallelism mechanism is especially useful for processing equi-join and range join queries. The joined columns of different tables typically share the same data semantics and the index
data of these columns are normally partitioned and distributed over
the index nodes in the same way. Therefore, these index nodes
can process the join queries in parallel. In addition, the support of
parallel scans of different indexes also facilitates correlated access
across multiple indexes, which is necessary when a query accesses
multiple indexed columns. Note that the indexing service only provides basic interfaces for upper layer applications to access the in-
dex data, while the join order between tables is determined by the
upper layer query optimizer such as the storage manager of a cloud
storage system [3] that includes the indexing service to extend its
functionalities.
3.3.3 Index Update
Client applications update the index via the interface of the framework. Receiving the update request from clients, the indexing service realizes this update in two steps. First, the corresponding old
index entries of the update are deleted from the system. Then, the
update is inserted into the indexes as a new index entry. The performance of update operations is studied in Appendix D.3.
It is notable that the enforcement of consistency and ACID properties for index update is based on the requirements of applications.
Since there is a trade-off between performance and consistency, the
client applications, based on its consistency requirements, will determine the policy to perform index updates. The indexes could be
updated under strict enforcement of ACID properties or in a less
demanding bulk update approach.
In the former approach, the client applications need to reflect all
modifications on the base records to the associated indexes before
returning acknowledgement messages to users. This approach typically requires the client applications to implement a refresh transaction in order to bring all associated index data up-to-date with
the base data. Since these data are possibly located on different
machines, an efficient distributed consensus protocol is more desirable than the traditional two-phase commit protocol. Paxos-based
algorithm has recently been shown as a more efficient alternative
approach [15].
In the latter approach, the client applications can backlog the
modification on the base records and bulk update these modifications to the associated indexes.In addition, the client applications
can dynamically determine the frequency of index updates in runtime based on the system workload. Specifically, when the client
application faces a peak load, i.e., a sudden increase in the input
load, it can defer the index bulk update to reserve system resources
for handling the user’s request first, and then resume the index bulk
update process after the peak load. We note that the problem of
guaranteeing ACID properties in the cloud is a broad research issue
itself [11] and developing an efficient strategy for the maintenance
of the proposed cloud indexing service is part of our future work.
3.4
System Performance and Availability
It is impractical for a user or upper layer application to do performance tuning with the existence of multiple types of indexes.
Therefore, we identify the factors that may affect the performances
for all types of indexes and apply general strategies to improve the
global performance of the system.
First, the index process routes queries based on the operators defined in the Cayley graph instances; however, it is expensive for
each process to maintain active network connections to all other
processes. Second, the memory capacity of the index process relative to the application size is limited and all the index entries cannot
be cached. To solve these issues, regardless of the index types, our
self tuning strategies optimize performance by adaptively creating
network connections and effectively buffering local indexes. We
describe these techniques in Appendix B.
In addition, the proposed indexing service is designed to meet
service level agreements (SLA) such as 24×7 system availability
– an important desideratum of cloud services, which requires the
system’s ability to handle failures on the index nodes. We describe
the replication of index data to ensure correct retrieval of data in
the presence of failures in Appendix C.
4. PERFORMANCE EVALUATION
We have run a series of experiments to evaluate the robustness,
efficiency and scalability of our proposed indexing framework. First,
we study the query performance with two query plans: index covering approach where the index entries contain a portion of the data
records to service the query request directly and index+base approach where the index entries only contain pointers to the records
in the base table.
Second, we compare the performance of distritbuted indexes against
parallel full table scans. Third, we study the scalability of the system in terms of both the system size and the number of indexes. In
Appendix D, we present additional experimental results on the effect of varying data size, the effect of varying query rate, the update
performance, the ability of handling skewed data and query distribution, and the performance of equi-join and range join query.
4.1 Experimental Setup
We test the indexing framework in two environments. We ran a
set of experiments in an in-house cluster to stress test the system
with varying query and update rates. The cluster includes 64 machines with Intel X3430 2.4 GHz processors, 8 GB of memory, 500
GB of disk capacity and gigabit ethernet.
We also conduct experiments on a cluster of commodity machines on Amazon EC2 to test the robustness and scalability of
the indexing framework when varying the system size from 16 to
256 nodes. Each index node in our system runs on a small instance
of EC2. This instance is a virtual machine with a 1.7 GHz Xeon
processor, 1.7 GB memory and 160 GB disk capacity.
We run most of experiments with TPC-W benchmark dataset2 .
TPC-W benchmark models the workload of a database application
where OLTP queries are common. These queries are relatively simple and selective in nature, and thus building indexes to facilitate
query processing is essential, especially in a large scale environment such as the cloud.
We generate 10 million to 160 million records (each record has
an average size of 1KB) of item table. Thus, the total data size
ranges from 10 GB to 160 GB. The data records are stored in
the underlying HDFS3 and sorted by their primary key, i.e., the
item id attribute. We build distributed indexes on the item title
attribute and the item cost attribute by respectively instantiating a
distributed hash index and distributed B+ -tree-like index based on
the proposed indexing framework. We test the performance of the
distributed indexes with two types of queries, namely exact match
query with a predicate on the item title attribute:
Q1:
SELECT item id FROM item WHERE item title =’ξ’
and range query with a predicate on the item cost attribute:
Q2:
SELECT item id FROM item
WHERE item cost > α AND item cost < β
By setting the values of α and β, we can define the selectivity of
the test queries.
In addition, to test the system with a bigger number of indexes,
we also synthetically generated data and indexes as follows. There
are multiple tables Ti with schema Ti (a1 , a2 , a3 , a4 , p) where each
attribute ai takes integer values that are randomly generated from
the domain of 109 values, and attribute p is a payload of 1 KB
data. Each table is generated with 10 million records. For each
table Ti , the attribute a1 is indexed with a distributed hash index,
a2 is indexed with a distributed B+ -tree-like index, and (a3 , a4 )
is indexed with a distributed multi-dimensional index. Thus, each
table Ti has 3 indexes, and we can test the effect of varying number
of indexes in the system by increasing the number of testing tables.
2
3
http://www.tpc.org/tpcw
http://hadoop.apache.org/hdfs
Query Latency (ms)
400
360
320
280
240
200
160
120
80
40
0
Index covering
Index+base
1
5
10
20
200
180
160
140
120
100
80
60
40
20
Full table (parallel) scan
Using index, s = 0.04%
Using index, s = 0.4%
Using index, s = 4%
10 20
40
# Records in Query Result
Figure 3: Index covering vs.
index+base
80
160
Data size (GB)
Figure 4: Index plan vs. full
table scan
Table 1 summarizes the default experiment configuration. The
default system size for the experiments is 64 index nodes. The
memory buffer for the local indexes at each node is set to 64 MB.
The system uses the adaptive connection management strategy as
the default setting. We test the system with the default 10 client
threads at each node. Each client thread continually submits a
workload of 100 operations to the system. A completed operation
will be immediately followed up by another operation. We also
vary the query rate and update rate submitted into the system by
changing the number of client threads at each node.
Table 1 Experiment Settings
Parameter
System size
Data size
Buffer size for local indexes
Number of client threads per node
Number of operations per thread
Query type
Query plan
4.2
Default
64
10 GB
64 MB
10
100
Exact match
Index covering
Min
16
10 GB
5
-
Max
256
160 GB
50
-
Index covering vs. Index+base Approach
In this experiment, we study the query processing performance
using distributed indexes with two alternative query plans, namely
index covering and index+base. In the former approach, the index
entries include the data of non-key attributes to service the queries
directly. For example, if the index entries of the distributed index
on item cost contain the item id information, then the above query
Q2 can be processed efficiently with only index traversal. On the
contrary, in the latter case, the query processing needs to follow the
pointers in the index entries and perform random reads on the base
table, which is costly when the base table is stored in the HDFS.
Figure 3 shows that the index covering approach outperforms the
index+base approach, especially when the the size of the query result set is large. Note that even though the index+base has worse
performance in this case, it still performs better than scanning the
whole table to retrieve only a few qualified data records. In our
experiment, even a parallel scan using MapReduce4 on the 10 GB
item table takes about 23 seconds (Figure 4), which is significantly
slower than the index+base approach. Moreover, it is also notable
that the cost of both index covering and index+base approach depend only on the size of the query result set, while the cost of full
(parallel) table scans increase with the table size.
In the extreme case of the index covering approach, users can
opt to include all the data of the original records in the index entries to speed up query processing. Although this approach incurs
additional storage cost, the query performance using the secondary
indexes is improved considerably. Moreover, the additional storage
cost is acceptable in the case the sizes of data records are relatively
small or we only include a portion of a data record that is needed
4
Query Latency (ms)
Query Latency (second)
100
90
80
70
60
50
40
30
20
10
0
http://hadoop.apache.org/mapreduce/
Query Throughput (in x 1000 ops/sec)
60
Exact match query
Range query, s=0.001%
Range query, s=0.002%
Range query, s=0.004%
50
40
Exact match query
Range query, s=0.001%
Range query, s=0.002%
Range query, s=0.004%
30
20
10
0
16 32
64
128
256
16 32
System size
Figure 5: Scalability test on
query latency (on EC2)
64
128
256
System size
Figure 6: Scalability test on
query throughput (on EC2)
for common queries. Hence, we mainly test the performance of the
system with the index covering query plan in other experiments.
4.3 Index plan vs. full table parallel scan
In this test, we vary the data set size from 10 GB to 160 GB (from
10 million to 160 million records). We compare the performance of
the system to process the query Q2 using the distributed B+ -treelike index with the approach that performs a full parallel scan on
the item table using MapReduce in a system of 64 cluster nodes.
As shown in Figure 4, when the data set size increases, the query
latency of the distributed index approach also increases due to the
increasing size of the result set. However, it still performs much
better than the full table scan approach, whose query response time
increases almost linearly along with the data set size.
The distributed index achieves better performance because it can
directly identify the qualified records and retrieve them from the
local indexes of the index nodes, while in the other approach the
whole table is scanned. The parallel scans with MapReduce still
consume a significant execution time when the table size is large.
Note that the distributed index also employs parallelism to speed
up query processing. When the query selectivity is set to 4% or
higher, the data that qualify the query could be stored on multiple
index nodes. These index nodes would perform the index scan in
parallel and the query latency would not increase with the size of
result set any longer.
4.4 Scalability test on EC2
In this experiment, we evaluate the scalability of the proposed indexing service in terms of the system size. We vary the system size
from 16 to 256 virtual machines on EC2 and measure the latency
and throughput of queries with different selectivities.
As can be seen from Figure 5, the system scales well with nearly
flat query latency when the system size increases. In our experimental setting, the workload submitted to the system is proportional to the system size. However, more workload can be handled
by adding more index nodes to the system. Therefore, the system
response time for a query request with respect to a specific query
selectivity is maintained nearly unchanged with different number of
index nodes. Figure 5 also shows that a query with lower selectivity
incurs higher latency, due to the larger result set, local processing
costs, and higher communication cost.
As the number of index nodes increases, the aggregated query
throughput also increases as shown Figure 6. In addition, the system query throughput scales almost linearly when the query has
high selectivity, especially for the exact-match query. With a high
query selectivity, the result set is small and therefore, the local processing at each index node and data transfer have less effect on the
query throughput. More importantly, the indexing service achieves
better throughput when there are more high selectivity queries for
its ability of being able to identify the qualified data quickly rather
than scanning multiple data nodes.
4.5
Multiple Indexes of Different Types
In this test, we experiment with 8 tables, each of which has 3
distributed indexes of the 3 different index types as described in
the experimental setup. The workload, i.e., the number of client
threads, submitted to the system is increased with the number of
indexes in the system (1 client thread for each index). We expect
more indexes in the system to be able to handle a bigger workload
from the users. Figure 7 and Figure 8 plot the effect of varying
the number of indexes on the query latency and system throughput
respectively.
Mixed Query Latency (ms)
160
140
120
100
80
60
40
20
0
Generalized index
One-overlay-per-index
80
60
40
20
0
6
12
18
Number of indexes
Figure 7: Query latency with
multiple indexes
24
Generalized index
One-overlay-per-index
[3]
[4]
[5]
[6]
6
12
18
24
Number of indexes
Figure 8: Query throughput
with multiple indexes
The results confirm the superiority of our generalized index over
the one-overlay-per-index approach that runs one overlay for a specific index, i.e., 24 overlays totally for 24 indexes in this test. The
generalized index can guarantee a constant query latency and its
query throughput increase steadily with the number of indexes that
it instantiates. This is due to the fact that with more indexes, there
will be more index traversal paths that can be used to answer the
queries. In addition, the query execution load is better shared among
the index nodes in the cluster.
While the generalized index approach only runs one index process to maintain multiple indexes and self-tunes the performance
among these indexes via sharing resources such as memory and network connections, the one-overlay-per-index approach runs multiple processes, each for a specific overlay. When there are more indexes, the more processes need to be launched, which considerably
adds overhead to the virtual machine and affects the query latency
and throughput. Therefore, our approach provides the much needed
scalability for supporting multiple indexes of different types in the
cloud.
5.
[2]
Mixed Query Throughput (in x1000 ops/sec)
120
100
6.[1] P.REFERENCES
Agrawal, A. Silberstein, B. F. Cooper, U. Srivastava, and
[7]
[8]
[9]
[10]
[11]
[12]
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[15]
CONCLUSION
This paper presents an extensible indexing framework to support
DBMS-like indexes in the cloud. The framework supports a set of
indexes using P2P overlays and provides a high level abstraction
for the definition of new indexes. The most distinguishing feature
of our scheme is the ability to support multiple types of distributed
indexes, such as hash, B+ -tree-like and multi-dimensional index,
in the same framework, which significantly reduces the maintenance cost and provides the much needed scalability. To achieve
this goal, we define two mapping functions to transform different
indexes into the Cayley graph instances. We exploit the characteristics of Cayley graph to reduce the index creation and maintenance
cost, and embed some self tuning capability. Finally, we evaluate
our indexing scheme in an in-house cluster and Amazon EC2 with
extensive experiments, which verify its efficiency and scalability.
Acknowledgment
The work in this paper was in part supported by the Singapore Ministry of Education Grant No. R-252-000-394-112 under the project
name of Utab. We would also like to thank the anonymous reviewers and the shepherd for their insightful comments.
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APPENDIX
A.
OVERLAY MAPPING
We had demonstrated how Chord [19] can be mapped to a Cayley
graph in Section 3.1. Here we discuss the mapping of BATON [7]
and CAN [16].
1. BATON
L
To support BATON overlay, x y is defined as (x + y)%2m
as well since BATON can be transformed to Chord by adding a
virtual node. In our case, the key space is [0, 2m − 1] and thus the
maximal level of BATON tree is m. Given a BATON node ni at
level l, suppose its ID at level l is x, ni can be transformed into a
node in Chord by using the following function:
θ(l, x) = 2m−l (2x − 1)
The routing neighbors of BATON are similar to those of Chord
except for the parent-child and adjacent links. If ni is a left child
of its parent, then the links to its parent node, right child and right
adjacent node can be emulated by I(ni ) + 2k . Since BATON has
a tree topology, ni ’s left adjacent link and left child link cannot be
emulated by Chord’s routing fingers, and therefore we define new
generators (2m − 2x , x is an integer) to handle the links. However,
to keep the framework generic, we choose to use the old generator
set, namely {2k |0 ≤ k ≤ m−1}. Even without half adjacent/child
links, we note that the queries can still be routed to the destination
node using a similar routing scheme as in Algorithm 1.
2. CAN
CAN partitions multi-dimensional space into zones such that
each zone is managed by a node. The kd-tree space partitioning
provides a good basis for multi-dimensional data indexing. Compared to other overlays, supporting CAN is more challenging, as
we need to establish a mapping between CAN’s identifiers (multidimensional vector) and Cayley graph’s key space (1-dimensional
value). There are many works on dimensionality reduction, such
as Space Filling Curve [9].The basic idea is to partition the search
space by each dimension iteratively, and assign a binary ID to each
sub-space, which is mapped to the Cayley graph based on its ID.
Similarly, a multi-dimensional query is transformed into a set of
sub-spaces, which are denoted
by their IDs as well.
L
In CAN, we define x y as x XOR y. The basic routing algorithm is shown in Algorithm 4. We first get the key space of current
node (lines 1 and 2). If the search key dest is covered by current
node, the lookup process can stop by returning current node (lines
3 and 4). Otherwise, we handle the lookup as in the following two
cases. First, if this is the first node receiving the search request,
the initial key start is empty. We iterate all keys in the node’s
key space to find the one, which has the longest common prefix
with the search key dest. That key will be used as the initial key
start (lines 5-10). Second, if the node is not the first node in the
search route, the initial key start has already been decided by the
last node in the route (lines 12 and 13). In either case, we attempt
to reduce the difference between dest and start by routing to a
property neighbor (lines 14 and 15).
B.
PERFORMANCE SELF TUNING
In Section 3.4 we identified the factors that influence the performance of the proposed framework. Here we discuss our solutions
to these issues.
B.1
Index Buffering Strategy
Each index process maintains the index data for different Cayley
Algorithm 4 CANLookup(Node ni , Key start, Key
dest)
1. Key k0 = I(ni .predecessor)
2. Key k1 = I(ni )
3. if dest > k0 and dest ≤ k1 then
4.
return ni
5. if start == N U LL then
6.
for i = k0 + 1 to k1 do
7.
p = getCommonP ref ix(i, dest)
8.
if p.length > maxlength then
9.
maxlength = p.length
10.
start = i
11. else
12.
p = getCommonP ref ix(start, dest)
13.
maxlength = p.length
14. Node nextN ode
=
getN odeByKey(start XOR
2maxlength+1 )
15. return nextN ode
graph instances. To support efficient retrieval of index data, given a
Cayley graph instance g, its index data, denoted as I(g), are stored
in a local disk-resident index structure of the index nodes. Based
on the type of g, different index structures are built for I(g). For
example, if g is a Chord [19] overlay, then a hash index is created.
Otherwise, if g is an instance of CAN [16], we create an R-tree
index for I(g). Similarly, a B+ -tree index is created if g is an
instance of BATON [7].
Figure 9 shows how the local indexes are maintained. In this
example, each index node is responsible for maintaining the index
data for three Cayley graph instances. We use the instance ID (IID)
to identify a specific instance in the Cayley graph manager.
Index node
Index node
Cayley graph overlay
Index node
Index node
Table
Indexed columns
IID
user
postcode
0
Local index
Hash
user
age, salary
2
R-tree
item
price
1
B-tree
...
...
...
...
Figure 9: Local Indexes
To improve the performance of the local disk-resident indexes
of each index node, we buffer some index entries, i.e., the nodes of
B+ -tree and R-tree, or buckets of hash index, in memory. However,
the available memory of the virtual machines hosting the indexing
service relative to the application size is limited. Therefore, each
index process establishes a buffer manager to manage the buffer
dynamically.
Let Idx = {e1 , e2 , ..., em } be all index entries on the disk,
where ei represents a node of B+ -tree and R-tree, or a bucket of
hash index. We define two functions to measure the importance
of an index entry. f (ei ) returns the number of queries involving
ei in last T seconds and g(ei ) is the size of ei . Suppose M bytes
are used to buffer the local indexes, we define a buffering vector
v = (v1 , v2 , ..., vm ). When ei is buffered in memory, vi is set to 1.
Otherwise, vi equals to 0. The buffer manager tries to find a buffer
vector that maximizes
m
X
vi f (ei )
i=1
and satisfies
m
X
vi g(ei ) ≤ M
i=1
This is a typical knapsack problem. We solve it using a greedy
algorithm. After every T seconds, we periodically run the above
algorithm to select the index entries for buffering. The old entries
are replaced by new ones to catch the query patterns.
B.2
Adaptive Network Connection
In our framework, the index process routes queries based on the
operators defined in the Cayley graph instances. The approach to
maintaining a complete connection graph is not scalable since each
index process can only maintain a limited number of open connections. Therefore, in our system a connection manager is developed
to manage the connections adaptively. It attempts to minimize the
routing latency by selectively maintaining the connections. The
connection manager classifies the connections as essential connections and enhanced connections. An essential connection is an active network connection established between two index processes
(Ip , Ip0 ) where Ip0 is a routing neighbor of Ip by the definition of any
Cayley graph instance in the Cayley graph manager. An enhanced
connections is established at runtime between two frequently communicating processes.
By maintaining essential connections, we keep the overlay structures defined by Cayley graph instances. Suppose K types of indexes are defined in the framework for a cluster of N nodes, each
node will maintain at most Klog2 N essential connections, with
log2 N connections for each type. That is, even if we have thousands of indexes defined for the tables using these K types of indexes, we will need only Klog2 N essential connections. Queries
can then be routed based on the overlay routing protocols with the
essential connections.
Enhanced connections can be considered as shortcuts for essential connections. When routing a message, the index process first
performs a local routing simulation using the Cayley graph information. Then, it checks the enhanced connections for shortcuts.
If no shortcut exists, it follows the normal routing protocols and
forwards the message via an essential connection. Otherwise, it
sends the message via the available enhanced connections, which
is adaptively created during query processing as follows.
To route a query, the connection manager performs a local routing simulation based on the Cayley graph information, and get a
path P which is a set of essential connections. We generate enhanced connections by replacing the chain of essential connections in P by a shortcut connection. Specifically, connection c =
(Ip , Ip0 ) is a candidate enhanced connection for P if there exists a
shortcut path P 0 of P , satisfying that P 0 ’s starting node is Ip and
its ending node is Ip0 .
The connection manager keeps a counter for each candidate connection, recording the number of appearances of the connection
during query processing. After every T seconds, the connection
manager discards current enhanced connections and adds the top
frequently used connections into the set of enhanced connections.
The counters are then reset to 0 and a new tuning iteration starts.
C.
FAILURES AND REPLICATION
While there could be fewer failures in a cloud environment relative to the churn experienced in a P2P system, machine failures in
large clusters are more common. Therefore, our indexing service
employs replication of index data to ensure the correct retrieval of
data in the presence of failures. Specifically, we use the two-tier
partial replication strategy to provide both data availability and load
balancing, as proposed in our recent study [20]. The first tier of
replication, which consists of totally K copies of the index data, is
designed to guarantee the data reliability requirement (K is commonly set to 3 in distributed systems with commodity servers [5,
15]). At the second tier, additional replicas of frequently accessed
data are adaptively created in runtime based on the query workload as a way to distribute the query load on the “hot” queried data
across their replicas.
Given a Cayley graph instance g, its index data, denoted as I(g),
are partitioned and distributed on multiple index nodes. The index
data on an index node (master replica) are replicated to the successors (slave replicas) of that index node. Note that the successors of
an index node regarding to a specific index are determined by the
type of g (e.g. Chord [19], BATON [7], CAN [16]), or more specifically, the operator of the Cayley graph (cf. Section 3.1). When the
master replica fails, we apply the Cayley graph operator to locate
its successors and retrieve the index data from one of these replicas.
Hence, the query processing of our indexing service is resilient to
the failures of index nodes.
Paxos-based replication algorithm [15] has been shown to be feasible to maintain strict consistency of replicas. However, the tradeoff is the complexity of the system and the performance of write operations. When the relaxed consistency is acceptable for client applications, the replicas can be maintained asynchronously instead.
The master replica is always updated immediately, while the update
propagation to slave replicas can be deferred until the index node
has spare network bandwidth and its peak load has passed.
To avoid the “lost updates” problem, i.e., the master replica crashes
while the update has not been propagated to other slave replicas, the
system performs write-ahead logging before updating the master
replica. Hence, in our indexing service, the updates to the master
replica of the index data are durable and eventually propagated to
the slave replicas. Note that if the master replica fails during the
processing of an update, its immediate successor will be promoted
to take over the mastership. Therefore, when an index node recovers from a failure, it can retrieve back all latest updates from the
slave replica that previously has been promoted to the mastership.
We studied the complete method for system recovery from various
types of node failures in [20].
D.
ADDITIONAL EXPERIMENTS
In this section, we present additional five sets of experimental
results: 1) the effect of varying data size 2) the effect of varying
query rate 3) the performance of update operations 4) the ability
of handling skewed data and query distribution and 5) the performance of equi-join and range join query. The default experimental
configuration is the same as described in Section 4.1.
D.1 Effect of Varying Data Size
In this experiment, we perform the scalability test on data size
and study the query performance in the system. Specifically, we
measure the latency of exact-match queries on the item title attribute, a non-key attribute of the item table. By instantiating a
distributed hash index on this attribute based on the proposed indexing framework, the system can support queries on this attribute
efficiently without the need of full table scan. As shown in Figure
10, the query response time using distributed indexes is not affected
by the database size.
Query Latency (ms)
Query Latency (ms)
threshold of 15 client threads per node, more queries will compete
for disk resources and the system throughput does not increase with
the input load any longer.
240
40
35
30
25
20
15
10
5
0
Adaptive cached connections
Point-to-point ad hoc connections
Exact match query
Range query, s=0.001%
Range query, s=0.002%
Range query, s=0.004%
200
160
D.3 Update Performance
120
80
40
0
10 20
40
80
5
160
10
15
20
25
30
35
40
45
50
# Threads per Client
Data size (GB)
Figure 10: Effect of varying Figure 11: Effect of varying
query rate
data size
In addition, the advantage of the proposed adaptive connection
management strategy is well demonstrated. The system can guarantee low query latency for users with the use of adaptive cached
connections. In this approach, each index node in the cluster keeps
a limited number of established connections to other frequently accessed nodes in the distributed index overlay. In this way, we do
not need to pay the cost of creating new connections which is the
norm in the case of ad-hoc point-to-point connection approach.
D.2 Effect of Varying Query Rate
In this test, we study the performance of exact match queries and
range queries using the distributed indexes when we vary the query
selectivity and the query input rate.
Figure 11 demonstrates that the system has better query latency
with higher query selectivity. This is due to the fact that with high
query selectivity, the result set is small and the system does not
need to spend much time to scan the local disk-resident index at
the index nodes in the cluster and retrieve the qualified records.
The results also show that the latency of exact-match queries is
less affected by input query rate than that of range queries. As
discussed above, range queries incur more local disk scans than an
exact-match query. When the input query rate is high, more queries
will compete with each other for the disk I/Os. Thus, the latency of
range queries increases with the query input rate.
Query Throughput (in x1000 ops/sec)
Query Throughput (in x1000 ops/sec)
120
Exact match query
640
560
480
400
320
240
160
80
Range query, s=0.001%
Range query, s=0.002%
Range query, s=0.004%
100
80
An update to the distributed indexes supported in our indexing
framework is performed in two steps. First, the corresponding old
index entries (if exists) of the update will be deleted from the system. Then, the update will be inserted into the indexes. Since the
old and the new index entry might reside on different machines we
need to perform two rounds of index traversal to process an update
request, which increases the network cost.
In addition, update operations might also need to modify the local disk-resident index pages. Thus, an update operation in the
indexes is much costlier than a search operation during query processing. Another source of latency cost of update operations is
the concurrency control on the local indexes, which we employ a
similar approach as Blink -tree [10], to guarantee the correctness of
concurrent updates.
In summary, the latency cost of an update to a distributed index
in our framework consists of three factors: the network cost, the
local index update cost, and the concurrency cost. We note that
regarding to the three types of distributed indexes implemented in
our framework, namely distributed hash, B+ -tree, and R-tree indexes, the network cost and concurrency cost of update operations
are similar. The only difference is the local index update cost,
which is dependent on the type of the local index, e.g., the local
hash table5 , B+ -tree6 and R-tree7 implemented for the distributed
indexes. Therefore, we shall present here the update performance
of the distributed hash index. We get similar observations on the
update performance of the distributed B+ -tree and R-tree index.
In this experiment, we test the update performance of the distributed hash index built on the item title attribute of the item
table in the 10 GB TPC-W benchmark data set. We perform scalability test with different system sizes on an in-house cluster and
measure the performance of update operations in term of the update
latency and update throughput. For each system size, we also vary
the input update load. Specifically, we launch from 5 to 50 client
threads at each node and each client thread continuously submits
update requests to the distributed index. Each completed operation
will be followed up by the another request.
60
Update Latency (ms)
40
20
5
10
15
20
25
30
35
40
45
# Threads per Client
Figure 12: Query throughput
50
5
10
15
20
25
30
35
40
45
50
# Threads per Client
Figure 13: Query throughput
More importantly, the advantage of our proposal is well demonstrated in Figure 12. The system achieves better load when there are
more concurrent exact match queries. With the use of indexes, we
facilitate better load distribution, since we do not have to scan all
nodes just to get the exact match tuples, and due to the ability of being able to identify the storage node that contains the tuple quickly,
we only search that node, and search it efficiently. Therefore, the
system can admit more queries and the throughput increases linearly along with the input load.
The system is also able to server better load when there are more
high selective range queries, e.g., 0.001%, as shown in Figure 13.
However, range queries with lower selectivities incur more local
disk scans, and thus the throughput of range queries is more constrained by the input load. Specifically, for range queries with selectivities 0.002% and 0.004%, when the input load reaches the
Update Throughput (in x1000 ops/sec)
40
35
30
25
20
15
10
5
0
100
90
80
70
60
50
40
30
20
5
10
15
20
25
30
35
40
45
# Threads per Client
Figure 14: Update latency
50
5
10
15
20
25
30
35
40
45
50
# Threads per Client
Figure 15: Update throughput
Figure 14 and Figure 15 plot the update performance of the distributed hash index in a system of 64 nodes. As we have discussed,
the update operation suffers from three considerable factors of latency cost. That is the reason why, in this test, the system is saturated when the input update rate is high, i.e., there is a large number
of client threads. In particular, the update throughput becomes stable when we increase the input rate to the level of 20 client threads
per node. When the input update load gets larger, there will be
5
http://sna-projects.com/krati/
www.oracle.com/technetwork/database/berkeleydb/overview/index.html
7
http://www.rtreeportal.org/code.html
6
more number of concurrent update operations in the system. These
operations compete each others for the resources such as disk I/Os
and concurrency lock holding. Therefore, given a fixed amount of
resources, i.e., 64 nodes in the cluster, the update performance is
constrained by a threshold of input load (about 20 client threads
per node in this experiment).
D.4 Handling Skewed Multi-Dimensional Data
In this test, we study the efficiency of our proposed indexing
system in the presence of skews both in data and query distribution.
We apply the Brinkhoff data generator8 to generate a dataset of 10
million skewed 2-d moving objects based on the city map, which
represents the real-time traffic.
System storage load distribution. The storage load of an index node is measured by the amount of index data maintained by
that index node. Since the data has skewed distribution, the use
of uniform data mapping function will assign some index nodes
with much more data than other nodes, leading to an unbalanced
system storage load distribution. This is the case where our proposed sampling-based data mapping takes its effect. As Figure 16
demonstrates, when the sampling-based data mapping function is
used, the system storage load is well distributed, i.e., a certain percentage of the number of index nodes (in the system of 64 nodes)
services the corresponding percentage of the index data.
Storage load distribution (%)
100
90
80
70
60
50
40
30
20
10
0
Sampling-based data mapping
Uniform data mapping
discussed in Section 3.3.2, the join order between multiple tables
is determined by the upper layer query optimizer, e.g. the storage
manager of a cloud storage system [3] that uses the indexing service to extend its functionalities.
Equi-join. In this test, we compare the equi-join performance
of two approaches: index join using the distributed indexes and
MapReduce-based sort merge join. The MapReduce join can be
implemented as follows. In the map phase, the mappers scan through
the two joining tables and with each tuple t the mappers generate an
intermediate records (kt ; t0 ) where kt is the joining key and t0 is tuple t tagged with the name of the table that it belongs to. The mappers then partition these intermediate records based on the value of
the joining key (a hash function is normally used to guarantee load
balance) and shuffle them to the reducers. In the reduce phase, the
reducers just need to form groups of the same key value and yield
the final join results.
To compare the performance of the two approaches, we measure
the latency of the following equi-join query based on the TPC-H9
schema:
SELECT O.orderkey, orderdate, L.partkey, quantity, shipdate
FROM Orders O, Lineitem L
WHERE O.orderkey = L.orderkey
and O.orderpriority=‘1-URGENT’
Query Latency (second)
2100
Maximum query load imbalance
350
1800
Sampling-based data mapping
Uniform data mapping
Query Latency (second)
150
Index join
MapReduce join
120
1500
1200
90
250
900
60
200
600
150
300
300
30
100
20
50
10 20 30 40 50 60 70 80 90 100
40
60
80
TPC-H Scale Factor
0
0
16
32
64
128
256
join selectivity = 1-10
join selectivity = 1-20
join selectivity = 1-40
100
0
10 20
40
80
160
Data size (GB)
The joined columns of different tables typically share the same
data semantics and the index data of these columns are normally
partitioned and distributed over the index nodes in the same manner. Therefore, to speed up the join query processing these index
nodes scan their local indexes and join the records in parallel. As
Figure 18: Index join vs. Figure 19: Range join perMapReduce join
formance
Figure 18 plots the experimental results when we vary the scales
of TPC-H benchmark in a cluster of 64 nodes. As expected, the
index join approach outperforms the MapReduce join approach because the indexes are able to identify the joinable records quickly
and join them in parallel on each index node. On the contrary,
the main shortcoming of the MapReduce join approach is the need
to transfer the whole base tables from the mappers to the reducers,
which incurs a great deal of overhead including network bandwidth
and storage capacity.
Range join. Since range join queries are not popularly tested in
benchmarks such as TPC-H, in this test we synthetically generate
data for two tables T1 and T2 with the same schema (rid, val, p)
where rid is the record id, val takes its values from the domain of
109 values and p is a payload of 1KB. These two tables are stored in
HDFS and we instantitate secondary indexes for both tables on the
val attribute using the distributed B+ -tree of the proposed indexing
framework. We measure the latency of the following range join
query on the val attribute:
SELECT T1 .rid, T2 .rid FROM T1 , T2
WHERE T1 .val between (T2 .val + α) and (T2 .val + β)
We define the join selectivity of the test queries, i.e., the average
number of the joining T2 records per T1 record, by setting the value
of α and β. Figure 19 shows the performance of using indexes for
processing range join queries with different selectivities and data
sizes in a system of 64 nodes. Note that the MapReduce-based sortmerge join is inefficient for processing equi-join queries as shown
previously. Extending it to support range join queries would only
reduce the performance, so we do not show its result in this test.
8
9
Percentage number of index nodes
Figure 16: Distribution of
load under skewed data distribution
System size
Figure 17: Load imbalance
under skewed query distribution
System execution load imbalance. The maximum query load
imbalance is defined as the ratio between the query execution load
of the heaviest-loaded node divided by the query execution load
of the lightest loaded node in the system. Figure 17 shows the
maximum query load imbalance of different system sizes under the
skewed query distribution (Zipf factor = 1).
In our experimental setup, a larger number of nodes in the system
results in a higher query workload input. The situation becomes
worse when the query distribution is skewed: an increasing number
of queries will be directed to some hot data. If the uniform data
mapping function is used while the data stored in the system has
skewed distribution, the system will end up with high imbalance in
query execution load.
On the contrary, the sampling-based data mapping function proposed in our indexing framework can roughly estimate the data distribution and distribute the data over the index nodes. Thus, the
incoming queries on the skewed data is also distributed over the
index nodes, leading to less query load imbalance in the system.
D.5 Performance of Equi-joins and Range Joins
http://www.fh-oow.de/institute/iapg/personen/brinkhoff/generator/
http://www.tpc.org/tpch/
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