Abstract
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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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