TY - JOUR

T1 - Faster multi-witnesses for Boolean matrix multiplication

AU - Gasieniec, Leszek

AU - Kowaluk, Mirosław

AU - Lingas, Andrzej

N1 - Funding Information:
E-mail addresses: L.A.Gasieniec@liverpool.ac.uk (L. Gąsieniec), kowaluk@mimuw.edu.pl (M. Kowaluk), Andrzej.Lingas@cs.lth.se (A. Lingas). 1 Research supported in part by the Royal Society International Joint Project, IJP – 2006/R2. 2 Research supported by the grant of the Polish Ministry of Science and Higher Education N20600432/0806. 3 Research supported in part by VR grant 621-2005-4806.

PY - 2009/1/31

Y1 - 2009/1/31

N2 - A generalization of the the k-witness problem of computing a single witness in a Boolean matrix multiplication, where k witnesses are determined for each positive entry of the Boolean product, is studied. It is also shown that k-witness problem can be deterministically solved in certain a time by an algorithm based on rectangular matrix multiplication. The bounded k-witness problem is a variant of the bounded k-reconstruction problem, in which all witnesses are recovered for entries that have at most k witnesses. The results also shows that The k-witness problem for the Boolean product of two n dimensional matrices can be deterministically solved in a certain time, by the algorithm using rectangular matrix multiplication. It is also found that the randomized algorithm for the k-witness problem matches the lower bound at the two extremes of the matrix.

AB - A generalization of the the k-witness problem of computing a single witness in a Boolean matrix multiplication, where k witnesses are determined for each positive entry of the Boolean product, is studied. It is also shown that k-witness problem can be deterministically solved in certain a time by an algorithm based on rectangular matrix multiplication. The bounded k-witness problem is a variant of the bounded k-reconstruction problem, in which all witnesses are recovered for entries that have at most k witnesses. The results also shows that The k-witness problem for the Boolean product of two n dimensional matrices can be deterministically solved in a certain time, by the algorithm using rectangular matrix multiplication. It is also found that the randomized algorithm for the k-witness problem matches the lower bound at the two extremes of the matrix.

KW - Algorithms

KW - Analysis of algorithms

KW - Boolean matrix multiplication

KW - Combinatorial problems

KW - Lowest common ancestors in dags

KW - Time complexity, directed acyclic graph (dag)

KW - Witnesses for Boolean matrix product

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U2 - 10.1016/j.ipl.2008.10.012

DO - 10.1016/j.ipl.2008.10.012

M3 - Article

AN - SCOPUS:59149098020

SN - 0020-0190

VL - 109

SP - 242

EP - 247

JO - Information Processing Letters

JF - Information Processing Letters

IS - 4

ER -