Competitive graph searches

We exemplify an optimization criterion for divide-and-conquer algorithms with a technique called generic competitive graph search. The technique is then applied to solve two problems arising from biocomputing, so-called Common Connected Components and Cograph Sandwich. The first problem can be defined as follows: given two graphs on the same set of n vertices, find the coarsest partition of the vertex set into subsets which induce connected subgraphs in both input graphs. The second problem is an instance of sandwich problems: given a partial subgraph G1 of G2, find a partial subgraph G of G2 that is partial supergraph of G1 (sandwich), and that is a cograph. For the former problem our generic algorithm not only achieves the current best known performance on arbitrary graphs and forests, but also improves by a log n factor when the input is made of planar graphs. However, our complexity for intervals graphs is slightly lower than a recent result. For the latter problem, we first study...

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Binh-Minh Bui-Xuan, Michel Habib, Christophe Paul
• Keywords: Common Connected Components, Competitive Graph Search, Partial Subgraph, TCS 2008, Theoretical Computer Science