TY - GEN

T1 - A fast and simple parallel algorithm for the monotone duality problem

AU - Boros, Endre

AU - Makino, Kazuhisa

PY - 2009

Y1 - 2009

N2 - We consider the monotone duality problem i.e., checking whether given monotone CNF φ and DNF ψ are equivalent, which is a prominent open problem in NP-completeness. We construct a fast and simple parallel algorithms for the problem, that run in polylogarithmic time by using quasi-polynomially many processors. The algorithm exhibits better parallel time complexity of the existing algorithms of Elbassioni [11]. By using a different threshold of the degree parameter ε of φ in the algorithm, we also present a stronger bound on the number of processors for polylogarithmic-time parallel computation and improves over the previously best known bound on the sequential time complexity of the problem in the case when the magnitudes of |φ|, |ψ| and n are different, e.g., |ψ|=|φ| α ≫ n for α>1, where n denotes the number of variables. Furthermore, we show that, for several interesting well-known classes of monotone CNFs φ such as bounded degree, clause-size, and intersection-size, our parallel algorithm runs polylogarithmic time by using polynomially many processors.

AB - We consider the monotone duality problem i.e., checking whether given monotone CNF φ and DNF ψ are equivalent, which is a prominent open problem in NP-completeness. We construct a fast and simple parallel algorithms for the problem, that run in polylogarithmic time by using quasi-polynomially many processors. The algorithm exhibits better parallel time complexity of the existing algorithms of Elbassioni [11]. By using a different threshold of the degree parameter ε of φ in the algorithm, we also present a stronger bound on the number of processors for polylogarithmic-time parallel computation and improves over the previously best known bound on the sequential time complexity of the problem in the case when the magnitudes of |φ|, |ψ| and n are different, e.g., |ψ|=|φ| α ≫ n for α>1, where n denotes the number of variables. Furthermore, we show that, for several interesting well-known classes of monotone CNFs φ such as bounded degree, clause-size, and intersection-size, our parallel algorithm runs polylogarithmic time by using polynomially many processors.

UR - http://www.scopus.com/inward/record.url?scp=70350402445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350402445&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02927-1_17

DO - 10.1007/978-3-642-02927-1_17

M3 - Conference contribution

AN - SCOPUS:70350402445

SN - 3642029264

SN - 9783642029264

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 183

EP - 194

BT - Automata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings

T2 - 36th International Colloquium on Automata, Languages and Programming, ICALP 2009

Y2 - 5 July 2009 through 12 July 2009

ER -