A Novel Algorithm for Finding Maximum Common Ordered Subgraph

In this paper, we study the following problem: given are adjacency matrices of two simple graphs. Find two principal matrices (though they are vectors) having the maximum inner product. When used for computing the similarity of two protein structures this problem is called contact map overlap and for the later, we give an exact B&B algorithm with bounds computed by solving Lagrangian relaxation of the problem. The efficiency of the approach is demonstrated on a popular benchmark set of instances together with a comparison with the best existing algorithm