A Polynomial-Time Algorithm for Computing the Maximum Common Subgraph of Outerplanar Graphs of Bounded Degree

Abstract

This paper considers the maximum common subgraph problem, which is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs. This paper presents a dynamic programming algorithm for computing the maximum common subgraph of two outerplanar graphs whose maximum vertex degree is bounded by a constant, where it is known that the problem is NP-hard even for outerplanar graphs of unbounded degree. Although the algorithm repeatedly modifies input graphs, it is shown that the number of relevant subproblems is polynomially bounded and thus the algorithm works in polynomial time.