A branch&cut algorithm for the maximum common edge subgraph problem

We investigate the Maximum Common Edge Subgraph Problem (MCES) defined as follows. Given two graphs G and H with the same number of vertices, find a common subgraph of G and H (not necessary induced) with the maximum number of edges. This problem arises in parallel programming environments, and was first defined by Bokhari in [S. Bokhari, On the mapping problem, IEEE Trans. Comput., C-30(3), 1981]. We present a new integer programming formulation for the MCES problem and carry out a polyhedral investigation of this model. A number of valid inequalities are identified, most of which are facet-defining. We also report on computational experiments.