Fast Boolean Matrix Multiplication for Highly Clustered Data
We consider the problem of computing the product of two n×n Boolean matrices A and B. For an n ×n Boolean matrix C, let G C be the complete weighted graph on the rows of C where the weight of an edge between two rows is equal to its Hamming distance, i.e., the number of entries in the first row having values different from the corresponding entries in the second one. Next, let MWT(C) be the weight of a minimum weight spanning tree of G C. We show that the product of A with B as well as the so called witnesses of the product can be computed in time õ(n(n + minMWT(A),MWT(B t )))1.
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