Maximum Common Subgraph: Upper Bound and Lower Bound Results

In bio informatics, the biological structure matching problems can be formulated as the problem of finding the maximum common subgraph. Among the many different variants of the maximum common subgraph problem, the maximum common induced subgraph of two graphs is of special interest. In this paper, first we derive the lower bound result for the exact algorithms of the maximum common induced subgraph of two graphs, based on the current research progress in the area of parameterized computation. Then we investigate the upper bound and design the approaches for addressing this problem. Basically, this problem can be reduced to find a maximum clique in the product graph of the two given graphs. In consideration of the upper bound result, the obtained lower bound result is asymptotically tight. We would like to point out that our lower bound result presented here is currently best-known