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Algorithms 2016, 9(1), 17; doi:10.3390/a9010017

Co-Clustering under the Maximum Norm

1
IGM-LabInfo, CNRS UMR 8049, Université Paris-Est Marne-la-Vallée, 77454 Marne-la-Vallée, France
2
Institut für Softwaretechnik und Theoretische Informatik, 10587 TU Berlin, Germany
This paper is an extended version of our paper published in Co-Clustering Under the Maximum Norm. In Proceedings of the 25th International Symposium on Algorithms and Computation (ISAAC’ 14), LNCS 8889, Jeonju, Korea, 15–17 December 2014; pp. 298–309.
*
Author to whom correspondence should be addressed.
Academic Editor: Javier Del Ser Lorente
Received: 7 December 2015 / Revised: 10 February 2016 / Accepted: 16 February 2016 / Published: 25 February 2016
View Full-Text   |   Download PDF [353 KB, uploaded 25 February 2016]   |  

Abstract

Co-clustering, that is partitioning a numerical matrix into “homogeneous” submatrices, has many applications ranging from bioinformatics to election analysis. Many interesting variants of co-clustering are NP-hard. We focus on the basic variant of co-clustering where the homogeneity of a submatrix is defined in terms of minimizing the maximum distance between two entries. In this context, we spot several NP-hard, as well as a number of relevant polynomial-time solvable special cases, thus charting the border of tractability for this challenging data clustering problem. For instance, we provide polynomial-time solvability when having to partition the rows and columns into two subsets each (meaning that one obtains four submatrices). When partitioning rows and columns into three subsets each, however, we encounter NP-hardness, even for input matrices containing only values from {0, 1, 2}. View Full-Text
Keywords: bi-clustering; matrix partitioning; NP-hardness; SAT solving; fixed-parameter tractability bi-clustering; matrix partitioning; NP-hardness; SAT solving; fixed-parameter tractability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Bulteau, L.; Froese, V.; Hartung, S.; Niedermeier, R. Co-Clustering under the Maximum Norm. Algorithms 2016, 9, 17.

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