An improved combinatorial algorithm for Boolean matrix multiplication

An Improved Combinatorial Algorithm for Boolean Matrix Multiplication

We present a new combinatorial algorithm for triangle finding and Boolean matrix multiplication that runs in Ô(n/ log n) time, where the Ô notation suppresses poly(loglog) factors. This improves the previous best combinatorial algorithm by Chan [4] that runs in Ô(n/ log n) time. Our algorithm generalizes the divide-and-conquer strategy of Chan’s algorithm. Moreover, we propose a general framewo...

A Practical Algorithm for Boolean Matrix Multiplication

Research on fast methods for multiplying two n x n Boolean matrices has followed two directions. On the one hand, there are the asymptotically fast methods derived from algorithms to multiply matrices with integer entries. On the other hand, it has been of interest to devise algorithms which, while inferior in the asymptotic sense, are simple enough to be advantageously implemented. This paper ...

Lower Bounds for Combinatorial Algorithms for Boolean Matrix Multiplication

In this paper we propose models of combinatorial algorithms for the Boolean Matrix Multiplication (BMM), and prove lower bounds on computing BMM in these models. First, we give a relatively relaxed combinatorial model which is an extension of the model by Angluin (1976), and we prove that the time required by any algorithm for the BMM is at least Ω(n/2 √ ). Subsequently, we propose a more gener...

Improved output-sensitive quantum algorithms for Boolean matrix multiplication

We present new quantum algorithms for Boolean Matrix Multiplication in both the time complexity and the query complexity settings. As far as time complexity is concerned, our results show that the product of two n× n Boolean matrices can be computed on a quantum computer in time Õ(n3/2+nl3/4), where l is the number of non-zero entries in the product, improving over the outputsensitive quantum a...

Some Combinatorial Aspects of Parallel Algorithm Design for Matrix Multiplication