A Polynomial-Time Algorithm for Computing the Maximum Common Subgraph of Outerplanar Graphs of Bounded Degree

This paper considers the maximum common subgraph problem, which is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs. This paper presents a dynamic programming algorithm for computing the maximum common subgraph of two outerplanar graphs whose maximum vertex degree is bounded by a constant, where it is known that the problem is NP-hard even for outerplanar graphs of unbounded degree. Although the algorithm repeatedly modifies input graphs, it is shown that the number of relevant subproblems is polynomially bounded and thus the algorithm works in polynomial time.

[1]  Andrzej Lingas,et al.  Faster Algorithms for Subgraph Isomorphism of \sl k -Connected Partial \sl k -Trees , 2000, Algorithmica.

[2]  Viggo Kann,et al.  On the Approximability of the Maximum Common Subgraph Problem , 1992, STACS.

[3]  T. Akutsu.  A Polynomial Time Algorithm for Finding a Largest Common Subgraph of almost Trees of Bounded Degree , 1993 .

[4]  Maciej M. SysŁ.  The subgraph isomorphism problem for outerplanar graphs , 1982 .

[5]  Maurice Bruynooghe,et al.  A Polynomial-time Metric for Outerplanar Graphs , 2007, MLG.

[6]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7]  Mario Vento,et al.  Thirty Years Of Graph Matching In Pattern Recognition , 2004, Int. J. Pattern Recognit. Artif. Intell..

[8]  Nagiza F. Samatova,et al.  The Maximum Common Subgraph Problem: Faster Solutions via Vertex Cover , 2007, 2007 IEEE/ACS International Conference on Computer Systems and Applications.

[9]  Mohammad Taghi Hajiaghayi,et al.  Subgraph isomorphism, log-bounded fragmentation, and graphs of (locally) bounded treewidth , 2007, J. Comput. Syst. Sci..

[10]  Jan Ramon,et al.  Frequent subgraph mining in outerplanar graphs , 2006, KDD '06.

[11]  Peter Willett,et al.  Maximum common subgraph isomorphism algorithms for the matching of chemical structures , 2002, J. Comput. Aided Mol. Des..

[12]  Svetha Venkatesh,et al.  Video indexing and similarity retrieval by largest common subgraph detection using decision trees , 2001, Pattern Recognit..

[13]  Xiuzhen Huang,et al.  Maximum common subgraph: some upper bound and lower bound results , 2006, BMC Bioinform..

[14]  Andrzej Lingas.  Subgraph Isomorphism for Biconnected Outerplanar Graphs in Cubic Time , 1989, Theor. Comput. Sci..

[15]  Kiyoko F. Aoki-Kinoshita,et al.  Finding the Maximum Common Subgraph of a Partial k-Tree and a Graph with a Polynomially Bounded Number of Spanning Trees , 2003, ISAAC.