TY - JOUR

T1 - Recognizing more unsatisfiable random k-sat instances efficiently

AU - Friedman, Joel

AU - Goerdt, Andreas

AU - Krivelevich, Michael

PY - 2006

Y1 - 2006

N2 - It is known that random k-SAT instances with at least cn clauses, where c = ck is a suitable constant, are unsatisfiable (with high probability). We consider the problem to certify efficiently the unsatisfiability of such formulas. A backtracking-based algorithm of Beame et al. [SIAM J. Comput., 31 (2002), pp. 1048-1075] shows that k-SAT instances with at least nk-1/(log n)k-3 clauses can be certified unsatisfiable in polynomial time. We employ spectral methods to improve on this bound. For even k ≥ 4 we present a polynomial time algorithm which certifies random k-SAT instances with at least n(k/2)+o(1) clauses as unsatisfiable (with high probability). For odd k we focus on 3-SAT instances and obtain an efficient algorithm for formulas with at least n3/2+ε clauses, where ε > 0 is an arbitrary constant.

AB - It is known that random k-SAT instances with at least cn clauses, where c = ck is a suitable constant, are unsatisfiable (with high probability). We consider the problem to certify efficiently the unsatisfiability of such formulas. A backtracking-based algorithm of Beame et al. [SIAM J. Comput., 31 (2002), pp. 1048-1075] shows that k-SAT instances with at least nk-1/(log n)k-3 clauses can be certified unsatisfiable in polynomial time. We employ spectral methods to improve on this bound. For even k ≥ 4 we present a polynomial time algorithm which certifies random k-SAT instances with at least n(k/2)+o(1) clauses as unsatisfiable (with high probability). For odd k we focus on 3-SAT instances and obtain an efficient algorithm for formulas with at least n3/2+ε clauses, where ε > 0 is an arbitrary constant.

KW - Random satisfiability

KW - Random structures

KW - Spectral methods

UR - http://www.scopus.com/inward/record.url?scp=33645781326&partnerID=8YFLogxK

U2 - 10.1137/S009753970444096X

DO - 10.1137/S009753970444096X

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AN - SCOPUS:33645781326

VL - 35

SP - 408

EP - 430

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 2

ER -