Unifying Graph Matching Problems with a Practical Solution

Recent advances in computer vision, information retrieval, and molecular biology amply demonstrate the value and importance of graph matching. However, graph matching algorithms developed to date are either application domainspecific or severely limited by the problem size. This paper presents a unified solution for the broad range of major graph matching problems. Particularly, the new algorithm goes beyond matching given pattern graphs and effectively tackles two very difficult graph matching problems -Maximal Common Subgraph and Maximal Overlap Sets. By mathematical proofs, these graph matching problems can be shown to be transformable into the maximum clique problem. This new algorithm actually alternates between clique-finding and graph coloring by utilizing the information generated from the counterpart to either solve the maximum clique problem or, alternatively, the graph coloring problem as well. The effectiveness of this algorithm to solve all these graph matching problems is then evaluated with an extensive set of benchmark graphs for clique finding. The solutions show consistent superior solution quality.