Bloom Based Filters for Hierarchical Data

1
Bloom Based Filters for Hierarchical Data

• Georgia Koloniari and Evaggelia Pitoura
  University of Ioannina, Greece

2
Outline

• Motivation
• Problem Description
• Related Work
• Our approach Multi-Level Bloom Filters
• Performance Evaluation
• Hierarchical Distribution of Filters
• Experimental Results
• Conclusions
• Future Work

3
Motivation

• Evolution of peer-to-peer systems as an effective
  way of sharing data
• Wide use of XML for data representation and
  exchange in the Internet
• Service Descriptions in XML-based languages
• Growing interest in content-based routing of data
• Challenge How to efficiently discover the
  appropriate data based on their content?

4
The Problem

• A peer-to-peer system where each node stores a
  set of XML documents
• A query issued at a node may need results from
  multiple nodes in the system
• Use data summaries at each node to assist query
  routing

B
SumB
A
C
SumC
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Summaries Requirements

• Scalability summaries should be able to scale to
  a large number of users and shared documents.
• Distribution should be distributed across the
  nodes of the peer-to-peer system without
  requiring any central point of control.
• Dynamic should support updates, since in a
  peer-to-peer system, users join and leave the
  system at will.

6
Related Work

• XML Indices
• The Index Fabric Cooper Shadmon, RightOrder
  Inc 2001
• XSKETCH Synopsis Polyzotis Garofalakis, VLDB
  2002
• APEX Chung, Min Chim, ACM SIGMOD 2002
• Path Tree Aboulnaga, Alameldeen Naughton, VLDB
  2001
• Signature-based Indices Park Kim, DASFAA 2001
• Routing in P2P
• Secure Service Discovery Hodes et al, Mobicom
  99
• Routing indices Crespo Garcia-Molina, ICDCS
  2002

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Data Model
ltxmlgt
ltdevicegt
ltprintergt
ltcolorgtlt/colorgt
ltpostscriptgtlt/postscriptgt
lt/printergt
ltcameragt
ltdigitalgtlt/digitalgt
lt/cameragt
lt/devicegt
lt/xmlgt
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Querying

• XML-based data or service descriptions
• Find the documents that satisfy a given query
• Queries that exploit content and structure of the
  data
• Membership Queries Is element X in set Y?
• Path Queries consisting of regular path
  expressions, i.e. device//camera

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Bloom Filters

• Compact data structures for a probabilistic
  representation of a set
• Appropriate to answer membership queries

10
Bloom Filters (contd)
Query for b check the bits at positions H1(b),
H2(b), ..., H4(b).
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Bloom Filters (contd)

• Appearance of false positives.
• False positive the probabilty that the filter
  recognizes an elemnt as belonging to the set
  although it does not.
• P (1 - e-kn/m)k
• Ease of updates with the use of an array of
  counters
• Unable to represent relationships between
  elements

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Our approach

• Bloom filters suitable for distributed
  environments
• Main drawback Unable to represent hierarchies
• Extend to multi-level Bloom Filters in order to
  support path queries
• Two approaches
• Breadth Bloom Filters
• Depth Bloom Filters

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Breadth Bloom Filters

• One Bloom Filter BBFi for each level of the tree
  i
• In each filter BBFi we insert the elements of all
  the nodes of level i.
• An additional BBF0 with all the elements to
  improve performance
• Different sizes of the filter for each filter
• Look-up
• check BBF0 for all elements of the path
• check each element ai of the path to the
  corresponding level

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Breadth Bloom Filters
BBF0
(device?printer?camera? color?postscript?digital)
BBF1
device
BBF2
printer ? camera
BBF3
(color?postscript?digital)
Queries device/printer/color
/printer/postscript
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Depth Bloom Filters

• One Bloom Filter DBFi for each path of the tree
  with length i, i.e. each path with i1 nodes
• In each DBFi we insert all paths of the tree
  with length i.
• Look-up for path of length p
• Check all elements of the query in DBF
• Check for every sub-path of length 2 to p
• For split the path at the positition of and
  check each sub-path seperately

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Depth Bloom Filters
(device?printer?camera? color?postscript?digital)

(device/printer?device/camera? camera/digital?prin
ter/color? printer/postscript)
(device/camera/digital ?device/printer/color ?devi
ce/printer/postscript)
Queries /device/printer/color
/device//postscript
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Experimental Evaluation

• 200 XML documents produced by the Niagara
  Generator (www.cs.wisc.edu/niagara)
• 4 hash functions using the MD5 message digest
  algorithm (RFC1321)
• Size of the filter 78000 bits, about 2 of the
  size of the documents
• Levels of the documents 4
• Elements per document 50
• No repetition between element names
• Length of queries 3 (e.g. /device/camera/digital)
  
• 90 of the elements forming the queries were
  contained in the documents
• Metric Percentage of false positives

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Influence of filter size
19
Influence of the number of elements per document
20
Influence of the levels of the document
21
Influence of the length of the queries
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Varying the query workload
Workload type /printer/digital
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Summary of Results

• Multi-level Bloom filters outperform Simple Bloom
  filters in evaluating path queries.
• For 2 of the total size of the data, multi-level
  Bloom filters evaluate path queries for a false
  positives ratio below 3, while Simple Blooms
  fail to recognize the correct paths, no matter
  how much the filter size increases.
• Breadth Blooms work better than Depth Blooms.
• Depth Blooms require more space but are suitable
  for handling queries for which Breadth Blooms
  present a high ratio of false positives (exp. 5)

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Distribution

• Each node stores
• local summary
• merged summary of neighbours
• merged summary constructed by applying the
  bit-wise OR per level
• Nodes organized according to topological
  proximity
• Two organizations of nodes
• hierarchical
• horizons

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Distribution Hierarchical Organization
Node C Local filter Merged filter E? F ? G ?
H Root filters A, B, D
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Bloom Filter Similarity

• Nodes organized according to Bloom Filter
  Similarity
• Measure similarity measure based on the
  Manhattan distance metric.
• Let two filters B and C of size m
• d(B, C) B1 C1 B2 C2 Bm
  Cm.
• similarity(B, C) m d(B, C).

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Bloom Filter Similarity (contd)
B
1
0
0
1
1
0
0
1
C
0
1
1
0
1
0
0
1
similarity(B, C) 8 - (1 0 0 1 0 1 0
1) 4
For multi-level Bloom filters similarity is
defined as the sum of each pair of corresponding
levels
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Content-Based Organization

• When a node joins the system
• it broadcasts its local summary and attaches to
  the most similar node available

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Performance in Distributed Setting

• Hierarchical organization of nodes
• Metric Number of hops
• Parameters
• Variable number of nodes
• Number of hierarchies 5
• Maximum out-degree 5
• Every 10 of all docs 70 similar
• Length of queries 2
• 10 of the documents have results
• 70 of the documents contain the elements of the
  path query
• One document per node

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Finding the first result with respect to the nodes
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Finding all the results with respect to the nodes
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Finding the first result with varying number of
results
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Finding the first result with respect to the nodes
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Finding all the results with respect to the nodes
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Summary of Results

• The content-based organization is much more
  efficient in finding all the results for a query,
  than the proximity organization.
• They both perform similarly in discovering the
  first result.
• The content-based organization outperforms the
  proximity one when the nodes that satisfy a given
  query are limited.
• Both Simple and multi-level Blooms can be
  efficiently used as distributed filters.
• For path queries, multi-level Blooms outperform
  Simple ones.

36
Conclusions

• We introduced two novel data structures Breadth
  and Depth Bloom Filters that exploit both the
  content and structure of the XML documents given
  a small space overhead.
• The new data structures outperform simple Bloom
  Filters with respect to false positives when
  addresing regular path expression queries
• Distributed in large-scale systems to support
  efficient service discovery
• Extended the use of Bloom filters to organize the
  nodes according to their content.

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Future Work

• Explore different policies for the filters
  distribution.
• Explore different types of data summaries (e.g.
  Signatures)
• Extend the data model to XML graphs and
  incorporate values into the indexes

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Thank you