2014 47th Hawaii International Conference on System Sciences (2008)

Waikoloa, Big Island, Hawaii

Jan. 7, 2008 to Jan. 10, 2008

ISSN: 1530-1605

ISBN: 0-7695-3075-3

pp: 475

ABSTRACT

A technique for clustering data by common attribute values involves grouping rows and columns of a binary matrix to make the minimum number of submatrices all 1.s. As binary matrices can be viewed as adjacency matrices of bipartite graphs, the problem is equivalent to partitioning a bipartite graph into the smallest number of complete bipartite sub-graphs (commonly called .bicliques.). We show that the Biclique Partition Problem (BPP) does not have a polynomial time a-approximation algorithm, for any a = 1, unless P=NP. We also show that the Biclique Partition Problem, restricted to whether at most k bicliques are sufficient (i.e. BPP(k)) for each positive integer k, has a polynomial time 2-approximation algorithm. In addition, we give an O(VE) time algorithm and BPP(2), and an O(V) algorithm to find an optimum biclique partition of trees.

INDEX TERMS

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CITATION

D. Bein,
I.H. Sudborough,
Z. Meng,
C.O. Shields, Jr.,
L. Morales,
W. Bein,
"Clustering and the Biclique Partition Problem",

*2014 47th Hawaii International Conference on System Sciences*, vol. 00, no. , pp. 475, 2008, doi:10.1109/HICSS.2008.504