Proceedings of the 41st Annual Hawaii International Conference on System Sciences (HICSS 2008) (2008)
Waikoloa, Big Island, Hawaii
Jan. 7, 2008 to Jan. 10, 2008
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.
D. Bein, I. Sudborough, Z. Meng, C. Shields, Jr., L. Morales and W. Bein, "Clustering and the Biclique Partition Problem," Proceedings of the 41st Annual Hawaii International Conference on System Sciences (HICSS 2008)(HICSS), Waikoloa, Big Island, Hawaii, 2008, pp. 475.