Efficient local search for very large-scale satisfiability problems
ACM SIGART Bulletin
On the greedy algorithm for satisfiability
Information Processing Letters
New ${\bf \frac{3}{4}}$-Approximation Algorithms for the Maximum Satisfiability Problem
SIAM Journal on Discrete Mathematics
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
Improved approximation algorithms for MAX SAT
Journal of Algorithms
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A new method for solving hard satisfiability problems
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
Tight bounds on local search to approximate the maximum satisfiability problems
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Pushing random walk beyond golden ratio
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
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The Local Search algorithm is one of the simplest heuristic algothms for solving the MAX-SAT problem. The goal of this paper is to estimate the relative error produced by this algorithm being applied to random 3-CNFs with fixed density $\varrho$. We prove that, for any $\varrho$, there is a constant c such that a weakened version of Local Search that we call One-Pass Local Search almost surely outputs an assignment containing cn+o(n) unsatisfied clauses. Then using a certain assumtion we also show this for Local Search. Although the assumption remains unproved the results well matches experiments.