Efficient transitive closure of sparse matrices over closed semirings

Authors:
Gerald Penn
Affiliations:
Department of Computer Science, University of Toronto, Toronto, Canada
Venue:
Theoretical Computer Science - Algebraic methods in language processing
Year:
2006

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Abstract

This paper surveys several alternative data structures and algorithms for multiplying sparse upper-triangular matrices over closed semirings, and evaluates their efficiency in computing transitive closures of matrices over the Boolean semiring. Two new variants are introduced that outperform previously known methods on a collection of large data-sets drawn from linguistic applications.