Planar Subgraph Isomorphism Revisited

Abstract. The problem of Subgraph Isomorphism is defined as follows: Given a pattern H and a host graph G on n vertices, does G contain a subgraph that is isomorphic to H? Eppstein [SODA 95, J’GAA 99] gives the first linear time algorithm for subgraph isomorphism for a fixed-size pattern, say of order k, and arbitrary planar host graph, improving upon the O(n √ k )-time algorithm when using the “Color-coding” technique of Alon et al [J’ACM 95]. Eppstein’s algorithm runs in time kO(k) n, that is, the dependency on k is superexponential. We improve the running time to 2O(k) n, that is, single exponential in k while keeping the term in n linear. Next to deciding subgraph isomorphism, we can construct a solution and count all solutions in the same asymptotic running time. We may enumerate ω subgraphs with an additive term O(ωk) in the running time of our algorithm. We introduce the technique of “embedded dynamic programming” on a suitably structured graph decomposition...

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: Frederic Dorn
• Keywords: Host Graph, Running Time, STACS 2010, Subgraph Isomorphism, Theoretical Computer Science