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

• Published in: Theoretical computer science Vol. 329; no. 1-3; pp. 1 - 45
• Main Authors: Coja-Oghlan, Amin, Goerdt, Andreas, Lanka, André, Schädlich, Frank
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 13.12.2004; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Combinatorics; Combinatorics. Ordered structures; Computer science; control theory; systems; Exact sciences and technology; Graph theory; Hypergraph discrepancy; Mathematics; Probabilistic analysis; Random k-SAT; Random MAX 2-SAT; Sciences and techniques of general use; Theoretical computing; Random k-SAT; Random MAX 2-SAT; Hypergraph discrepancy; Probabilistic analysis; Hypergraph; Algorithm theory; Random MAX 2 SAT; Computer theory; Random k SAT; Combinatorial algorithm; Approximation algorithm; Polynomial time
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2004.07.017

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⩾Cn2 for a sufficiently large constant C>0. In addition, we present an algorithm based on the Lovász ϑ function that decides within polynomial expected time whether Formn,k,m is satisfiable, provided that k is even and m⩾C·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⩾Cn.