The complexity of Boolean matrix root computation

Authors:
Martin Kutz
Affiliations:
Freie Universität Berlin, Germany
Venue:
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Year:
2003

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Abstract

We show that finding roots of Boolean matrices is an NP-hard problem. This answers a twenty year old question from semigroup theory. Interpreting Boolean matrices as directed graphs, we further reveal a connection between Boolean matrix roots and graph isomorphism, which leads to a proof that for a certain subclass of Boolean matrices related to subdivision digraphs, root finding is of the same complexity as the graph-isomorphism problem.