On selecting a satisfying truth assignment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Noise strategies for improving local search
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
On the approximation of maximum satisfiability
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for NP-hard problems
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Reactive search, a history-sensitive heuristic for MAX-SAT
Journal of Experimental Algorithmics (JEA)
Finding almost-satisfying assignments
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Parameterizing above guaranteed values: MaxSat and MaxCut
Journal of Algorithms
On the run-time behaviour of stochastic local search algorithms for SAT
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Improved approximation algorithms for MAX SAT
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
New upper bounds for maximum satisfiability
Journal of Algorithms
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
SAT Local Search Algorithms: Worst-Case Study
Journal of Automated Reasoning
New Worst-Case Upper Bounds for SAT
Journal of Automated Reasoning
Local Search Algorithms for SAT: An Empirical Evaluation
Journal of Automated Reasoning
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
Solving Boolean Satisfiability Using Local Search Guided by Unit Clause Elimination
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
An Improved Exponential-Time Algorithm for k-SAT
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT
Discrete Applied Mathematics - The renesse issue on satisfiability
Using CSP look-back techniques to solve real-world SAT instances
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Evidence for invariants in local search
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Tuning local search for satisfiability testing
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Confronting hardness using a hybrid approach
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A new algorithm for optimal 2-constraint satisfaction and its implications
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Tight bounds on local search to approximate the maximum satisfiability problems
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
MAX-SAT for formulas with constant clause density can be solved faster than in O(2n) time
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
A survey of approximation results for local search algorithms
Efficient Approximation and Online Algorithms
Approximating MAX SAT by moderately exponential and parameterized algorithms
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
An exponential time 2-approximation algorithm for bandwidth
Theoretical Computer Science
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During the past 3 years there was a considerable growth in the number of algorithms solving MAX-SAT and MAX-2-SAT in worst-case time of the order cK, where c K is the number of clauses of the input formula. However, similar bounds w.r.t. the number of variables instead of the number of clauses are not known.Also, it was proved that approximate solutions for these problems (even beyond inapproximability ratios) can be obtained faster than exact solutions. However, the corresponding exponents still depended on the number of clauses of the input formula. In this paper, we give a randomized (1 - ε)-approximation algorithm for MAX-k-SAT whose worst-case time bound depends on the number of variables.Our algorithm and its analysis are based on Schöning's proof of the best current worst-case time bound for k-SAT (in: Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, FOCS'99, 1999, pp. 410-414). Similarly to Schöning's algorithm (which is also very close to Papadimitriou's algorithm (in: Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91, 1991, pp. 163-169) and the experimentally successful WalkSAT family by Selman et al. (in: Proceedings of the AAAI'97, 1997, pp. 321-326; in: Proceedings of the 12th National Conference on Artificial Intelligence, AAAI'94, 1994, pp. 337-343)), our algorithm makes random walks of polynomial length. We prove that the probability of error in each walk is at most 1 - ck,ε-N, where N is the number of variables, and Ck,ε k and ε. Therefore, making ⌈-ln ρ⌉ck,εN such walks gives the probability of error bounded from above by any predefined constant ρ 0.