The Maximum Common Subgraph (MCS) problem appears in many guises and in a wide variety of applications. The usual goal is to take as inputs two graphs, of order m and n, respectively, and find the largest induced subgraph contained in both of them. MCS is frequently solved by reduction to the problem of finding a maximum clique in the order mn association graph, which is a particular form of product graph built from the inputs. In this paper a new algorithm, termed "clique branching," is proposed that exploits a special structure inherent in the association graph. This structure contains a large number of naturally-ordered cliques that are present in the association graph's complement. A detailed analysis shows that the proposed algorithm requires O((m + 1)n) time, which is a superior worst-case bound to those known for previously-analyzed algorithms in the setting of the MCS problem. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Suters, W. H., Abu-Khzam, F. N., Zhang, Y., Symons, C. T., Samatova, N. F., & Langston, M. A. (2005). A new approach and faster exact methods for the maximum common subgraph problem. In Lecture Notes in Computer Science (Vol. 3595, pp. 717–727). Springer Verlag. https://doi.org/10.1007/11533719_73
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