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Issue No.05 - May (1994 vol.43)

pp: 629-633

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.280812

ABSTRACT

<p>A simple decomposition of a r/spl times/c/spl lcub/0,1/spl rcub/-matrix is defined in terms of a collection of disjoint submatrices obtained by deleting a "minimal" set of columns. In general, the number of such simple decompositions is /spl Theta/(2/sup r/). A class of matrices, namely, vertex-tree graphic, is defined, and it is shown that the number of simple decompositions of a vertex-tree graphic matrix is at most r/spl minus/1. Finally, the relevance of simple decomposition to the well-known problem of cluster formation on /spl lcub/0,1/spl rcub/-matrices is uncovered, and an O(r/sup 2/c) time algorithm is given to solve this problem for vertex-tree graphic matrices.</p>

INDEX TERMS

matrix algebra; matrices; decomposition; disjoint submatrices; cluster formation; cluster decomposition; cluster-formation problem; disconnecting set; edge-tree graphic matrix; vertex-tree graphic matrix.

CITATION

R. Swaminathan, "Decomposition of {0,1}-Matrices",

*IEEE Transactions on Computers*, vol.43, no. 5, pp. 629-633, May 1994, doi:10.1109/12.280812