Multivalent Graph Matching Problem Solved by Max-Min Ant System

Kieu Diem Ho, Jean-Yves Ramel, Nicolas Monmarché

Abstract: This paper presents a multivalent graph matching problem and proposes a max-min ant system for its resolution. Multivalent graph matching is a very combinatorial problem where a node (edge) in one graph can match with more than one node (edge) in the other graph. We formalize this problem as an extended graph edit distance problem by adding possibilities of splitting and merging operations. Then, we employ an ant colony based optimization algorithm, the max-min ant system, to solve this very combinatorial problem. A local search is also integrated to enhance the solution quality. The efficiency of the proposed approach is verified on a symbol data set in several aspects. The results show that the proposed approach can be very useful in case of noise when the bijective graph matching-based approaches are not usually robust.