Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k-SAT

by: Amin Coja-Oghlan, Andreas Goerdt, Andre Lanka, Frank Schadlich

Theoretical Computer Science, Vol. 329, No. 1-3. (13 December 2004), pp. 1-45.

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Abstract

We apply techniques from the theory of approximation algorithms to the problem of deciding whether a random k-SAT formula is satisfiable. Let Formn,k,m denote a random k-SAT instance with n variables and m clauses. Using known approximation algorithms for MAX CUT or MIN BISECTION, we show how to certify that Formn,4,m is unsatisfiable efficiently, provided that m[greater-or-equal, slanted]Cn2 for a sufficiently large constant C>0. In addition, we present an algorithm based on the Lovasz [theta] function that decides within polynomial expected time whether Formn,k,m is satisfiable, provided that k is even and m[greater-or-equal, slanted]C[middle dot]4knk/2. Finally, we present an algorithm that approximates random MAX 2-SAT on input Formn,2,m within a factor of 1-O(n/m)1/2 in expected polynomial time, for m[greater-or-equal, slanted]Cn.

@article{citeulike:139140, abstract = {We apply techniques from the theory of approximation algorithms to the problem of deciding whether a random k-SAT formula is satisfiable. Let Formn,k,m denote a random k-SAT instance with n variables and m clauses. Using known approximation algorithms for MAX CUT or MIN BISECTION, we show how to certify that Formn,4,m is unsatisfiable efficiently, provided that m[greater-or-equal, slanted]Cn2 for a sufficiently large constant C>0. In addition, we present an algorithm based on the Lovasz [theta] function that decides within polynomial expected time whether Formn,k,m is satisfiable, provided that k is even and m[greater-or-equal, slanted]C[middle dot]4knk/2. Finally, we present an algorithm that approximates random MAX 2-SAT on input Formn,2,m within a factor of 1-O(n/m)1/2 in expected polynomial time, for m[greater-or-equal, slanted]Cn.}, author = {Coja-Oghlan, Amin and Goerdt, Andreas and Lanka, Andre and Schadlich, Frank }, citeulike-article-id = {139140}, doi = {http://dx.doi.org/10.1016/j.tcs.2004.07.017}, journal = {Theoretical Computer Science}, keywords = {sat}, month = {December}, number = {1-3}, pages = {1--45}, posted-at = {2005-03-24 15:09:12}, priority = {2}, title = {Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k-SAT}, url = {http://dx.doi.org/10.1016/j.tcs.2004.07.017}, volume = {329}, year = {2004} }

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TY - JOUR ID - citeulike:139140 L3 - citeulike-article-id:139140 N2 - We apply techniques from the theory of approximation algorithms to the problem of deciding whether a random k-SAT formula is satisfiable. Let Formn,k,m denote a random k-SAT instance with n variables and m clauses. Using known approximation algorithms for MAX CUT or MIN BISECTION, we show how to certify that Formn,4,m is unsatisfiable efficiently, provided that m[greater-or-equal, slanted]Cn2 for a sufficiently large constant C>0. In addition, we present an algorithm based on the Lovasz [theta] function that decides within polynomial expected time whether Formn,k,m is satisfiable, provided that k is even and m[greater-or-equal, slanted]C[middle dot]4knk/2. Finally, we present an algorithm that approximates random MAX 2-SAT on input Formn,2,m within a factor of 1-O(n/m)1/2 in expected polynomial time, for m[greater-or-equal, slanted]Cn. IS - 1-3 JF - Theoretical Computer Science EP - 45 TI - Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k-SAT VL - 329 SP - 1 KW - sat AU - Coja-Oghlan, Amin AU - Goerdt, Andreas AU - Lanka, Andre AU - Schadlich, Frank PY - 2004/12/13/ UR - http://dx.doi.org/10.1016/j.tcs.2004.07.017 ER -

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