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Finding maximum edge bicliques in convex bipartite graphs

Nussbaum, D ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1007/s00453-010-9486-x
  3. Publisher: Springer , 2012
  4. Abstract:
  5. 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 edge biclique can be computed in O(na(n)) and O(n) time, respectively, where n = min(|A|, |B|) and a(n) is the slowly growing inverse of the Ackermann function
  6. Keywords:
  7. Convex bipartite graphs ; Ackermann functions ; Bicliques ; Biconvex graphs ; Bipartite graphs ; Bipartite permutation graphs ; Convex-bipartite ; DNA microarray data ; Graph G ; Subgraphs ; Time bound ; Graphic methods ; Graph theory
  8. Source: Algorithmica ; Volume 64, Issue 2 , October , 2012 , Pages 311-325 ; 01784617 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00453-010-9486-x