Graph Indexing: A Frequent Structure- based Approach Alicia Cosenza November 26 th, 2007.

Graph Indexing: A Frequent Structure-based Approach

Alicia Cosenza

November 26th, 2007

Presentation Outline

IntroductionFrequent FragmentDiscriminative FragmentGindex Experimental Result

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

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

Presentation Outline

IntroductionFrequent FragmentDiscriminative FragmentGindex Experimental Result

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

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!

Presentation Outline

IntroductionFrequent FragmentDiscriminative FragmentGindex Experimental Result

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

xF

x f F f x fD D

x F

x f F f x fD D

Presentation Outline

IntroductionFrequent FragmentDiscriminative FragmentGindex Experimental Result

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

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

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

GIndex - Search

GIndex - Search

Optimization Apriori Pruning

– If a fragment is not in the gIndex tree, we need not check its super-graphs

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

GIndex – Maintenance

Presentation Outline

IntroductionFrequent FragmentDiscriminative FragmentGindex Experimental Result

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.

Experimental Result

Data is from an AIDS Antiviral Screen Dataset

Experimental Result

The End