A new approach and faster exact methods for the maximum common subgraph problem

Authors:
W. Henry Suters;Faisal N. Abu-Khzam;Yun Zhang;Christopher T. Symons;Nagiza F. Samatova;Michael A. Langston
Affiliations:
Department of Mathematics and Computer Science, Carson-Newman College, Jefferson City, TN;Division of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon;Department of Computer Science, University of Tennessee, Knoxville, TN;Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN;Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN;Department of Computer Science, University of Tennessee, Knoxville, TN
Venue:
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Year:
2005

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Abstract

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.