Finding maximum edge bicliques in convex bipartite graphs

Authors:
Doron Nussbaum;Shuye Pu;Jörg-Rüdiger Sack;Takeaki Uno;Hamid Zarrabi-Zadeh
Affiliations:
School of Computer Science, Carleton University, Ottawa, Ontario, Canada;Hospital for Sick Children, Toronto, Ontario, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;National Institute of Informatics, Tokyo, Japan;School of Computer Science, Carleton University, Ottawa, Ontario, Canada
Venue:
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Year:
2010

Citing 18
Cited 1

A log log n data structure for three-sided range queries

Information Processing Letters
Computing a perfect edge without vertex elimination ordering of a chordal bipartite graph

Information Processing Letters
On the consecutive ones property

Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing

Theoretical Computer Science
On bipartite and multipartite clique problems

Journal of Algorithms
Relations between average case complexity and approximation complexity

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Formal Concept Analysis: Mathematical Foundations

Formal Concept Analysis: Mathematical Foundations
Biclustering of Expression Data

Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
The maximum edge biclique problem is NP-complete

Discrete Applied Mathematics
Biclustering Algorithms for Biological Data Analysis: A Survey

IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Consensus algorithms for the generation of all maximal bicliques

Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
Generating bicliques of a graph in lexicographic order

Theoretical Computer Science
On the generation of bicliques of a graph

Discrete Applied Mathematics
Algorithms for Maximum Independent Set in Convex Bipartite Graphs

Algorithmica
Enumeration aspects of maximal cliques and bicliques

Discrete Applied Mathematics
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

Journal of Computer and System Sciences
Inapproximability of maximum weighted edge biclique and its applications

TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Dynamic matchings in convex bipartite graphs

MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science

Solving the maximum edge biclique packing problem on unbalanced bipartite graphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.