Finding maximum edge bicliques in convex bipartite graphs

A bipartite graph G=(A, B, E) is convex on B if there exists an ordering of the vertices of B such that for any vertex v εA, vertices adjacent to v are consecutive in B. A complete bipartite subgraph of a graph G is called a biclique of G. In this paper, we study the problem of finding the maximum edge-cardinality biclique in convex bipartite graphs. Given a bipartite graph G=(A, B, E) which is convex on B, we present a new algorithm that computes the maximum edge-cardinality biclique of G in O(n log3 n loglogn) time and O(n) space, where n=|A|. This improves the current O(n 2) time bound available for the problem

Finding maximum edge bicliques in convex bipartite graphs

A bipartite graph G = (A,B,E) is convex on B if there exists an ordering of the vertices of B such that for any vertex v ? A, vertices adjacent to v are consecutive in B. A complete bipartite subgraph of a graph G is called a biclique of G. Motivated by an application to analyzing DNA microarray data, we study the problem of finding maximum edge bicliques in convex bipartite graphs. Given a bipartite graph G = (A,B,E) which is convex on B, we present a new algorithm that computes a maximum edge biclique of G in O(nlog3 n log log n) time and O(n) space, where n = |A|. This improves the current O(n 2) time bound available for the problem. We also show that for two special subclasses of convex bipartite graphs, namely for biconvex graphs and bipartite permutation graphs, a maximum ed