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
Discovering local structure in gene expression data: the order-preserving submatrix problem
Proceedings of the sixth annual international conference on Computational biology
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Biclustering of Expression Data
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
A New Clustering Method for Microarray Data Analysis
CSB '02 Proceedings of the IEEE Computer Society Conference on Bioinformatics
The maximum edge biclique problem is NP-complete
Discrete Applied Mathematics
Machine Learning
Biclustering Algorithms for Biological Data Analysis: A Survey
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Algorithms and theory of computation handbook
Finding maximum edge bicliques in convex bipartite graphs
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Low-Rank Matrix Approximation with Weights or Missing Data Is NP-Hard
SIAM Journal on Matrix Analysis and Applications
A mixed graph model for community detection
International Journal of Intelligent Information and Database Systems
Utility-maximizing event stream suppression
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
Dense subgraph mining with a mixed graph model
Pattern Recognition Letters
Domination analysis of algorithms for bipartite boolean quadratic programs
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Solving the maximum edge biclique packing problem on unbalanced bipartite graphs
Discrete Applied Mathematics
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Given a bipartite graph G = (V1, V2, E) where edges take on both positive and negative weights from set S, the maximum weighted edge biclique problem, or S-MWEB for short, asks to find a bipartite subgraph whose sum of edge weights is maximized. This problem has various applications in bioinformatics, machine learning and databases and its (in)approximability remains open. In this paper, we show that for a wide range of choices of S, specifically when |min S/max S| ∈ Ω(ηδ-1/2) ∩ O(η1/2-δ) (where η = max{|V1|, |V2|}, and δ ∈ (0, 1/2), no polynomial time algorithm can approximate S-MWEB within a factor of nƐ for some Ɛ 0 unless RP = NP. This hardness result gives justification of the heuristic approaches adopted for various applied problems in the aforementioned areas, and indicates that good approximation algorithms are unlikely to exist. Specifically, we give two applications by showing that: 1) finding statistically significant biclusters in the SAMBA model, proposed in [18] for the analysis of microarray data, is nƐ-inapproximable; and 2) no polynomial time algorithm exists for the Minimum Description Length with Holes problem [4] unless RP = NP.