Co-Clustering under the Maximum Norm

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}.
Document type :
Journal articles
Complete list of metadatas

Cited literature [15 references]  Display  Hide  Download
Contributor : Laurent Bulteau <>
Submitted on : Friday, March 24, 2017 - 12:41:28 PM
Last modification on : Monday, December 10, 2018 - 3:24:04 PM
Long-term archiving on : Sunday, June 25, 2017 - 1:11:26 PM


Publisher files allowed on an open archive



Laurent Bulteau, Vincent Froese, Sepp Hartung, Rolf Niedermeier. Co-Clustering under the Maximum Norm. Algorithms, MDPI, 2016, 9 (1), pp.15 - 17. ⟨10.3390/a9010017⟩. ⟨hal-01494976⟩



Record views


Files downloads