TY - GEN

T1 - The probabilistic analysis of a greedy satisfiability algorithm

AU - Kaporis, Alexis C.

AU - Kirousis, Lefteris M.

AU - Lalas, Efthimios G.

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

PY - 2002

Y1 - 2002

N2 - Consider the following simple, greedy Davis-Putnam algorithm applied to a random 3-CNF formula of constant density c: Arbitrarily set to TRUE a literal that appears in as many clauses as possible, irrespective of their size (and irrespective of the number of occurrences of the negation of the literal). Reduce the formula. If any unit clauses appear, then satisfy their literals arbitrarily, reducing the formula accordingly, until no unit clause remains. Repeat. We prove that for c< 3.42 a slight modification of this algorithm computes a satisfying truth assignment with probability asymptotically bounded away from zero. Previously, algorithms of increasing sophistication were shown to succeed for c< 3.26. Preliminary experiments we performed suggest that c≈3.6 is feasible running algorithms like the above, which take into account not only the number of occurrences of a literal but also the number of occurrences of its negation, irrespectively of clause-size information.

AB - Consider the following simple, greedy Davis-Putnam algorithm applied to a random 3-CNF formula of constant density c: Arbitrarily set to TRUE a literal that appears in as many clauses as possible, irrespective of their size (and irrespective of the number of occurrences of the negation of the literal). Reduce the formula. If any unit clauses appear, then satisfy their literals arbitrarily, reducing the formula accordingly, until no unit clause remains. Repeat. We prove that for c< 3.42 a slight modification of this algorithm computes a satisfying truth assignment with probability asymptotically bounded away from zero. Previously, algorithms of increasing sophistication were shown to succeed for c< 3.26. Preliminary experiments we performed suggest that c≈3.6 is feasible running algorithms like the above, which take into account not only the number of occurrences of a literal but also the number of occurrences of its negation, irrespectively of clause-size information.

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U2 - 10.1007/3-540-45749-6_51

DO - 10.1007/3-540-45749-6_51

M3 - Conference contribution

AN - SCOPUS:84938084560

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

SP - 574

EP - 586

BT - Algorithms - ESA 2002 - 10th Annual European Symposium, Proceedings

A2 - Möhring, Rolf

A2 - Raman, Rajeev

PB - Springer Verlag

T2 - 10th Annual European Symposium on Algorithms, ESA 2002

Y2 - 17 September 2002 through 21 September 2002

ER -