Tight Bounds on Local Search to Approximate the Maximum Satisfiability Problems

2011 ◽  
pp. 49-61 ◽  
Author(s):  
Daming Zhu ◽  
Shaohan Ma ◽  
Pingping Zhang
Keyword(s):  
Local Search ◽  
Maximum Satisfiability ◽  
Satisfiability Problems

scholarly journals Solving Set Cover and Dominating Set via Maximum Satisfiability

2020 ◽  
Vol 34 (02) ◽  
pp. 1569-1576 ◽  
Author(s):  
Zhendong Lei ◽  
Shaowei Cai
Keyword(s):  
Local Search ◽  
Large Scale ◽  
Dominating Set ◽  
Scoring Function ◽  
Initial Solution ◽  
Set Covering ◽  
Set Cover ◽  
Covering Problem ◽  
Greedy Heuristic ◽  
Maximum Satisfiability

The Set Covering Problem (SCP) and Dominating Set Problem (DSP) are NP-hard and have many real world applications. SCP and DSP can be encoded into Maximum Satisfiability (MaxSAT) naturally and the resulting instances share a special structure. In this paper, we develop an efficient local search solver for MaxSAT instances of this kind. Our algorithm contains three phrase: construction, local search and recovery. In construction phrase, we simplify the instance by three reduction rules and construct an initial solution by a greedy heuristic. The initial solution is improved during the local search phrase, which exploits the feature of such instances in the scoring function and the variable selection heuristic. Finally, the corresponding solution of original instance is recovered in the recovery phrase. Experiment results on a broad range of large scale instances of SCP and DSP show that our algorithm significantly outperforms state of the art solvers for SCP, DSP and MaxSAT.

scholarly journals Low-Rank Semidefinite Programming for the MAX2SAT Problem

2019 ◽  
Vol 33 ◽  
pp. 1641-1649
Author(s):  
Po-Wei Wang ◽  
J. Zico Kolter
Keyword(s):  
Semidefinite Programming ◽  
State Of The Art ◽  
Search Algorithm ◽  
Low Rank ◽  
Search Methods ◽  
Maximum Satisfiability ◽  
Satisfiability Problems ◽  
Theoretical Tool ◽  
Recent Approach ◽  
Programming Techniques

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete or incomplete solver, and we demonstrate on a variety of problems from recent competitions. Our experiments show that the approach is faster (sometimes by orders of magnitude) than existing state-of-the-art complete and incomplete solvers, representing a substantial advance in search methods specialized for MAX2SAT problems.

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