Finding Maximum Common Connected Subgraphs Using Clique Detection or Constraint Satisfaction Algorithms

This paper investigates the problem of Maximum Common Connected Subgraph (MCCS) which is not necessarily an induced subgraph. This problem has so far been neglected by the literature which is mainly devoted to the MCIS problem. Two reductions of the MCCS problem to a MCCIS problem are explored: a classic method based on linegraphs and an original approach using subdivision graphs. Then we propose a method to solve MCCS that searchs for a maximum clique in a compatibility graph. To compare with backtrack approach we explore the applicability of Constraint Satisfaction framework to the MCCS problem for both reductions.

[1]  H. C. Johnston.  Cliques of a graph-variations on the Bron-Kerbosch algorithm , 2004, International Journal of Computer & Information Sciences.

[2]  J. J. McGregor,et al.  Backtrack search algorithms and the maximal common subgraph problem , 1982, Softw. Pract. Exp..

[3]  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.

[4]  Frank Harary,et al.  Graph Theory , 2016 .

[5]  Ina Koch,et al.  Enumerating all connected maximal common subgraphs in two graphs , 2001, Theor. Comput. Sci..

[6]  G. Levi.  A note on the derivation of maximal common subgraphs of two directed or undirected graphs , 1973 .

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

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

[9]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[10]  Thomas Schiex,et al.  Soft Constraints , 2000, WLP.

[11]  H. Whitney.  Congruent Graphs and the Connectivity of Graphs , 1932 .

[12]  Panos M. Pardalos,et al.  Handbook of combinatorial optimization. Supplement , 2005 .

[13]  Toby Walsh,et al.  Handbook of Constraint Programming , 2006, Handbook of Constraint Programming.

[14]  Coenraad Bron,et al.  Finding all cliques of an undirected graph , 1973 .

[15]  Panos M. Pardalos,et al.  The maximum clique problem , 1994, J. Glob. Optim..

[16]  C. Bron,et al.  Algorithm 457: finding all cliques of an undirected graph , 1973 .

[17]  Peter van Beek,et al.  Principles and Practice of Constraint Programming - CP 2005, 11th International Conference, CP 2005, Sitges, Spain, October 1-5, 2005, Proceedings , 2005, CP.

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

[19]  Javier Larrosa,et al.  Constraint satisfaction algorithms for graph pattern matching , 2002, Mathematical Structures in Computer Science.

[20]  Yves Deville,et al.  CP(Graph): Introducing a Graph Computation Domain in Constraint Programming , 2005, CP.

[21]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.