1. Xifeng Yan Philip S. Yu Jiawei Han SIGMOD 2005 Substructure Similarity Search in Graph Databases

2. Outlines Motivation Objectives Methodology - Grafil - Feature-based structural filtering - Feature Set Selection Experiments Conclusions 2

3. Motivation Exact matching is often too restrictive, similarity search of complex structures becomes a vital operation. Substructure similarity computation is very expensive, practically it is not affordable in a large database. 3

4. Objectives Substructure similarity search using indexed features. Transforming the edge relaxation ratio of a query graph into the maximum allowed missing features, called Grafil. Filter many graphs without performing pairwise similarity computations. 4

5. Search Categories 5 Full structure search: find the structure exactly the same as the query graph. Substructure search: find structures that contain the query graph. Full structure similarity search: find structures that are similar to the query graph.

6. Methodology 6

7. Grafil (Graph Similarity Filtering) 7

8. Example: Relaxation Ratio 8

9. Feature-based structural filtering 9

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11. 11 No matter which edge is relaxed, the relaxed query graph should have at least two occurrences of these features. (upper bound of feature misses is written as ) Relaxed query graph may miss at most four occurrences of these features in comparison with the original query graph which have six occurrences: one fa, one fb, four fc. We can discard graphs that do not contain at least two occurrences of these features.

12. Feature Graph Matrix Index 12

13. Substructure similarity search divide into four part 13

14. Feature Set Selection 14

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17. Experiment 17

18. Conclusions 18 Explored the filtering algorithm using indexed structural patterns, without doing costly structure comparisons. We identify the criteria to form effective feature sets for filtering, and combining features with similar size and selectivity can improve the filtering and search performance significantly.