A New Approach and Faster Exact Methods for the Maximum Common Subgraph Problem

  • W. Henry Suters
  • Faisal N. Abu-Khzam
  • Yun Zhang
  • Christopher T. Symons
  • Nagiza F. Samatova
  • Michael A. Langston
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3595)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • W. Henry Suters
    • 1
  • Faisal N. Abu-Khzam
    • 2
  • Yun Zhang
    • 3
  • Christopher T. Symons
    • 4
  • Nagiza F. Samatova
    • 4
  • Michael A. Langston
    • 3
  1. 1.Department of Mathematics and Computer ScienceCarson-Newman CollegeJefferson CityUSA
  2. 2.Division of Computer Science and MathematicsLebanese American UniversityBeirutLebanon
  3. 3.Department of Computer ScienceUniversity of TennesseeKnoxvilleUSA
  4. 4.Computer Science and Mathematics DivisionOak Ridge National LaboratoryOak RidgeUSA

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