Fast algorithms for anti-distance matrices as a generalization of Boolean matrices
Abstract
We show that Boolean matrix multiplication, computed as a sum of products of column vectors with row vectors, is essentially the same as Warshall's algorithm for computing the transitive closure matrix of a graph from its adjacency matrix. Warshall's algorithm can be generalized to Floyd's algorithm for computing the distance matrix of a graph with weighted edges. We will generalize Boolean matrices in the same way, keeping matrix multiplication essentially equivalent to the Floyd-Warshall algorithm. This way, we get matrices over a semiring, which are similar to the so-called "funny matrices". We discuss our implementation of operations on Boolean matrices and on their generalization, which make use of vector instructions.
Cite
@article{arxiv.1705.08743,
title = {Fast algorithms for anti-distance matrices as a generalization of Boolean matrices},
author = {Michiel de Bondt},
journal= {arXiv preprint arXiv:1705.08743},
year = {2017}
}
Comments
10 pages + g++ template header files; minor corrections + friend class declarations added