Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
On Diameter Verification and Boolean Matrix Multiplication.
On Diameter Verification and Boolean Matrix Multiplication.
A Geometric Approach to Boolean Matrix Multiplication
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
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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 GC 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 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)})).