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. 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 log log n) time and O(n) space, where n = |A|. This improves the current O(n2) time bound available for the problem.

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