Genetic Approximate Matching of Attributed Relational Graphs Thomas Bärecke¹, Marcin Detyniecki¹, Stefano Berretti² and Alberto Del Bimbo² ¹ Université Pierre et Marie Curie - Paris6 UMR 7606, DAPA, LIP6, Paris, France ² Università degli Studi di Firenze, Dipartimento di Sistemi e Informatica, Florence, Italy

T. Bärecke et al. Genetic Approximate Matching of ARGs 2 Motivation 1/2 Frontal Neutral expression

T. Bärecke et al. Genetic Approximate Matching of ARGs 3 Motivation 2/2

T. Bärecke et al. Genetic Approximate Matching of ARGs 4 Outline EC Subgraph Isomorphism Genetic Approach  Encoding  Crossover  Local search  Combination with tree search Results Conclusions and Future Work

T. Bärecke et al. Genetic Approximate Matching of ARGs 5 EC (Sub-)Graph Isomorphism No known optimal and efficient algorithm Genetic algorithms  “Parallel” exploration of large non-continuous search spaces  No perfect exploitation  Adaptive stop criterion Solution quality Elapsed time  Good solutions in reasonable time Optimal algorithms  Exponential complexity  Max. 15 vertices

T. Bärecke et al. Genetic Approximate Matching of ARGs 6 GA - Encoding

T. Bärecke et al. Genetic Approximate Matching of ARGs 7 GA - Crossover Fitness change depends on all other elementary mappings Strict position-based crossover (PBX)

T. Bärecke et al. Genetic Approximate Matching of ARGs 8 Strict position-based crossover Create position list and shuffle it Uniformly select crossover points Create children  In case of collision place in alternative place  Fill in missing values XxxXxx

T. Bärecke et al. Genetic Approximate Matching of ARGs 9 GA – Local Search Neighborhood N Fitness evaluation of the neighborhood

T. Bärecke et al. Genetic Approximate Matching of ARGs 10 GA – other parameters NameValue Tournament size2 Termination10 Crossover probability0.9 Mutation probability0 2-opt probability1 Population size100 UPMX ratio0.33 Elitism1

T. Bärecke et al. Genetic Approximate Matching of ARGs 11 Combining GA with A* … … GA … …

T. Bärecke et al. Genetic Approximate Matching of ARGs 12 Outline EC Subgraph Isomorphism Genetic Approach Results  Evolution  Precision  Run time  Combined method Conclusions and Future Work

T. Bärecke et al. Genetic Approximate Matching of ARGs 13 Evolution Process False MappingsFitness

T. Bärecke et al. Genetic Approximate Matching of ARGs 14 Diversity

T. Bärecke et al. Genetic Approximate Matching of ARGs 15 Precision – Crossover 1/2 PBXPMX

T. Bärecke et al. Genetic Approximate Matching of ARGs 16 Precision – Crossover 2/2 PBXUPMX

T. Bärecke et al. Genetic Approximate Matching of ARGs 17 Results - Runtime Graph size Noise (Size 50)

T. Bärecke et al. Genetic Approximate Matching of ARGs 18 Combined results

T. Bärecke et al. Genetic Approximate Matching of ARGs 19 Conclusions Permutation based Genetic Algorithm  Robust for Subgraph Matching  Crossover operator  Local search  Solution candidate at any time Combination of exact and approximate methods

T. Bärecke et al. Genetic Approximate Matching of ARGs 20 Future Work Real world data! Allow more graph edit operations Better local improvement heuristic Fewer and optimal parameters Comparison with cycle crossover

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