Graph Indexing: A Frequent Structure-based Approach

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Graph Indexing A Frequent Structure-based
Approach

• Alicia Cosenza
• November 26th, 2007

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Presentation Outline

• Introduction
• Frequent Fragment
• Discriminative Fragment
• Gindex
• Experimental Result

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Introduction

• Graphs are used to model complicated structures
  such as proteins, circuits, images and XML
  documents
• Current index approach is path based
• Example GraphGrep
• Advantages
• Paths are easier to handle
• Index space is predefined all the path up to
  maxL length are selected
• Disadvantages
• Path is too simple
• There are too many paths and too many false
  positives

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Introduction

• Can we use a graph structure instead of a a path
  as the basic index feature?
• gIndex
• Indexes only frequent subgraphs
• Creates a smaller index
• Improves query times

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Presentation Outline

• Introduction
• Frequent Fragment
• Discriminative Fragment
• Gindex
• Experimental Result

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Frequent Fragment

• Key concept
• Fragment small subgraph
• minsup minimum support threshold
• A graph is frequent if its support or the number
  of times it appears in the graph database is
  greater than minsup
• Only frequent fragments will be indexed

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Frequent Fragment

• low minimum support on small fragments (for
  effectiveness)
• Want to index lots of the small subgraphs
• high minimum support on large fragments (for
  compactness)
• Only want to index a large fragment if it appears
  a lot
• Otherwise it will be indexed by the smaller
  subgraphs
• Problem There could be a lot of frequent
  fragments!

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Presentation Outline

• Introduction
• Frequent Fragment
• Discriminative Fragment
• Gindex
• Experimental Result

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Discriminative Fragment

• Definition (Redundant Fragment)
• Fragment is redundant with respect to
  feature set if
• Definition (Discriminative Fragment).
• Fragment is discriminative with respect to
  if
• Fragments that are not redundant are called
  discriminative

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Presentation Outline

• Introduction
• Frequent Fragment
• Discriminative Fragment
• Gindex
• Experimental Result

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GIndex - Construction

• First generates all frequent fragments while
  taking out redundant ones
• Translates fragments into sequences and holds
  them in a prefix tree
• Each fragment has an id list the ids of the
  graphs containing the fragment
• Graph Sequentialization (DFS Code)
• Labeled edge is a 5-tuple (I,j,li, l(I,j),lj)
• Described in another paper

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GIndex - Construction

• gIndex Tree
• each fragment can be mapped to an edge sequence
  (DFS code), insert the edge sequences of
  discriminative fragments in a prefix tree called
  the gIndex Tree

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GIndex - Construction

• gIndex Tree
• Implemented using a hash table
• Both black and white nodes are included in the
  table
• The tree is still an important concept since it
  determines what white nodes will be included

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GIndex - Search
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GIndex - Search

• Optimization
• Apriori Pruning
• If a fragment is not in the gIndex tree, we need
  not check its super-graphs

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GIndex - Search

• Verification
• After getting the candidate answer set, we have
  to verify that the graphs in the set really
  contain the query graph
• perform a subgraph isomorphism test on each graph
  one by one

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GIndex Maintenance
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Presentation Outline

• Introduction
• Frequent Fragment
• Discriminative Fragment
• Gindex
• Experimental Result

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Experimental Result

• The index size of gIndex is more than 10 times
  smaller than that of GraphGrep
• gIndex outperforms GraphGrep by 3 to 10 times in
  various query loads
• the index returned by the incremental maintenance
  algorithm is effective it performs as well as
  the index computed from scratch provided the data
  distribution does not change much.

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Experimental Result

• Data is from an AIDS Antiviral Screen Dataset

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Experimental Result
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The End