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Random Walk with Continuously Smoothed Variable Weights
- In Proceedings of SAT-2005
, 2005
"... Abstract. Many current local search algorithms for SAT fall into one of two classes. Random walk algorithms such as Walksat/SKC, Novelty+ and HWSAT are very successful but can be trapped for long periods in deep local minima. Clause weighting algorithms such as DLM, GLS, ESG and SAPS are good at esc ..."
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Cited by 14 (2 self)
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Abstract. Many current local search algorithms for SAT fall into one of two classes. Random walk algorithms such as Walksat/SKC, Novelty+ and HWSAT are very successful but can be trapped for long periods in deep local minima. Clause weighting algorithms such as DLM, GLS, ESG and SAPS are good at escaping local minima but require expensive smoothing phases in which all weights are updated. We show that Walksat performance can be greatly enhanced by weighting variables instead of clauses, giving the best known results on some benchmarks. The new algorithm uses an efficient weight smoothing technique with no smoothing phase. 1
Efficient 2 and 3-Flip Neighborhood Search Algorithms for the MAX SAT
- Journal of Heuristics
, 1998
"... . For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most eective approaches. Most of the local search algorithms are based on the 1-ip neighborhood, which is the set of solutions obtainable by ipping the truth assignment of one variable. In this paper, w ..."
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Cited by 13 (2 self)
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. For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most eective approaches. Most of the local search algorithms are based on the 1-ip neighborhood, which is the set of solutions obtainable by ipping the truth assignment of one variable. In this paper, we consider r-ip neighborhoods for r 2, and propose, for r = 2; 3, new implementations that reduce the number of candidates in the neighborhood without sacricing the solution quality. For 2-ip (resp., 3-ip) neighborhood, we show that its expected size is O(n + m) (resp., O(m + t 2 n)), which is usually much smaller than the original size O(n 2 ) (resp., O(n 3 )), where n is the number of variables, m is the number of clauses and t is the maximum number of appearances of one variable. Computational results tell that these estimates by the expectation well represent the real performance. These neighborhoods are then used under the framework of tabu search etc., and compa...
Analyses on the 2 and 3-Flip Neighborhoods for the MAX SAT
- Journal of Combinatorial Optimization
, 1999
"... For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most eective approaches. Most of the local search algorithms are based on the 1-ip neighborhood, which is the set of solutions obtainable by ipping the truth assignment of one variable. In this paper, we cons ..."
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Cited by 5 (2 self)
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For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most eective approaches. Most of the local search algorithms are based on the 1-ip neighborhood, which is the set of solutions obtainable by ipping the truth assignment of one variable. In this paper, we consider r-ip neighborhoods for r 2, and propose, for r = 2; 3, new implementations that reduce the number of candidates in the neighborhood without sacri cing the solution quality. For 2-ip (resp., 3-ip) neighborhood, we show that its expected size is O(n + m) (resp., O(m+ t n)), which is usually much smaller than the original size O(n ) (resp., O(n )), where n is the number of variables, m is the number of clauses and t is the maximum number of appearances of one variable. Computational results tell that these estimates by the expectation well represent the real performance.
Speculative Pruning for Boolean Satisfiability
, 1998
"... Much recent work on boolean satisfiability has focussed on incomplete algorithms that sacrifice accuracy for improved running time. Statistical predictors of satisfiability do not return actual satisfying assignments, but at least two have been developed that run in linear time. Search algorithm ..."
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Much recent work on boolean satisfiability has focussed on incomplete algorithms that sacrifice accuracy for improved running time. Statistical predictors of satisfiability do not return actual satisfying assignments, but at least two have been developed that run in linear time. Search algorithms allow increased accuracy with additional running time, and can return satisfying assignments. The efficient search algorithms that have been proposed are based on iteratively improving a random assignment, in effect searching a graph of degree equal to the number of variables. In this paper, we examine an incomplete algorithm based on searching a standard binary tree, in which statistical predictors are used to speculatively prune the tree in constant time. Experimental evaluation on hard random instances shows it to be the rst practical incomplete algorithm based on tree search, surpassing even graph-based methods on smaller instances.
