An Improved Maximum Common Induced Subgraph Solver

One of the traditional ways of solving the maximum common induced subgraph problem is by reduction to a maximum clique problem. The two input graphs, in which the maximum common subgraph is to be found, are multiplied to form a product graph, which is then input to the maximum clique algorithm. The result of the latter are used to identify the nodes of the input graphs that form the maximum common subgraph. Although the maximum clique problem can be solved by a modern branch-and-bound based algorithm for general graphs, such approach is far from optimal. Some special properties of the product graph can be exploited to guide the maximum clique search. Namely, the modern state-of-the-art clique search programs use coloring as auxiliary algorithm, but finding a good coloring of a graph itself a hard task. In this article, we use the exploit the nature of the product graph to provide the maximum clique algorithm with a very good initial coloring or multiple such colorings. We perform experiments on a large database of small to medium sized graphs and demonstrate the efficiency of the proposed method against a state of the art method for solving maximum common subgraph problem.