Fast boolean matrix multiplication for highly clustered data

Abstract

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 GCbe 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, letMWT(C) be the weight of a minimum weight spanning tree of GC. 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 + min{MWT(A),MWT(Bt)})).