Maximal common connected sets of interval graphs

Abstract

Given a pair of graph G1 = (V, E1), G2 = (V, E2) on the same vertex set, a set S ⊆ V is a maximal common connected set of G1 and G2 if the subgraphs of G 1 and G2 induced by 5 are both connected and S is maximal the inclusion order. The maximal Common Connected sets Problem (CCP for short) consists in identifying the partition of V into maximal common connected sets of G1 and G2. This problem has many practical applications, notably in computational biology. Let n = |V| and m = |E1| + |E 2|. We present an O((n + m) log n) worst case time algorithm solving CCP when G1 and G2 are two interval graphs. The algorithm combines maximal clique path decompositions of the two input graphs together with an Hopcroft-like partitioning approach. © Springer-Verlag 2004.