research-article

GRASP: A Search Algorithm for Propositional Satisfiability

Authors:

João P. Marques-Silva,

Karem A. SakallahAuthors Info & Claims

IEEE Transactions on Computers, Volume 48, Issue 5

Pages 506 - 521

https://doi.org/10.1109/12.769433

Published: 01 May 1999 Publication History

Abstract

This paper introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), a new search algorithm for Propositional Satisfiability (SAT). GRASP incorporates several search-pruning techniques that proved to be quite powerful on a wide variety of SAT problems. Some of these techniques are specific to SAT, whereas others are similar in spirit to approaches in other fields of Artificial Intelligence. GRASP is premised on the inevitability of conflicts during the search and its most distinguishing feature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack nonchronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by recording the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straightforward bookkeeping of the causality chains leading up to conflicts allows GRASP to identify assignments that are necessary for a solution to be found. Experimental results obtained from a large number of benchmarks indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances.

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Cited By

Dao TVrain C(2024)A review on declarative approaches for constrained clusteringInternational Journal of Approximate Reasoning10.1016/j.ijar.2024.109135171:COnline publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1016/j.ijar.2024.109135
Osama MWijs ABiere A(2024)Certified SAT solving with GPU accelerated inprocessingFormal Methods in System Design10.1007/s10703-023-00432-z62:1-3(79-118)Online publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1007/s10703-023-00432-z
Marques-Silva J(2024)Logic-Based Explainability: Past, Present and FutureLeveraging Applications of Formal Methods, Verification and Validation. Software Engineering Methodologies10.1007/978-3-031-75387-9_12(181-204)Online publication date: 27-Oct-2024
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Index Terms

GRASP: A Search Algorithm for Propositional Satisfiability
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
2. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Randomness, geometry and discrete structures

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Reviews

Reviewer: Linda Pagli

This is yet another work on backtrack heuristics to solve the NP-complete satisfiability problem (SAT), without any attempt to analytically evaluate the quality of the results. Still, the proposed new GRASP algorithm is very interesting from the point of view of algorithm design and engineering. Some clever mechanisms allow pruning of the search tree to a point that the performance of GRASP on major benchmarks is outstanding. The paper is well organized and clearly written. The initial sections provide a review of SAT structure and its solution disciplines, with proper bibliographic pointers. The implemented procedure for conflict analysis is then discussed thoroughly. The great value of the paper is evident in section 4, where the organization and the results of a vast experiment are presented convincingly. We can fairly conclude that, on the average, GRASP practically outperforms all of the other known algorithms on a rich collection of major benchmarks. Because of its plain style and good organization, the paper can be read by nonspecialists, although it will probably raise a strong interest only in the community of SAT enthusiasts.

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Published In

cover image IEEE Transactions on Computers

IEEE Transactions on Computers Volume 48, Issue 5

May 1999

96 pages

ISSN:0018-9340

Editor:
Jean-Luc Gaudiot
Univ. of Southern California, Los Angeles

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Copyright © Copyright © 1999 IEEE. All Rights Reserved.

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IEEE Computer Society

United States

Publication History

Published: 01 May 1999

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Dao TVrain C(2024)A review on declarative approaches for constrained clusteringInternational Journal of Approximate Reasoning10.1016/j.ijar.2024.109135171:COnline publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1016/j.ijar.2024.109135
Osama MWijs ABiere A(2024)Certified SAT solving with GPU accelerated inprocessingFormal Methods in System Design10.1007/s10703-023-00432-z62:1-3(79-118)Online publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1007/s10703-023-00432-z
Marques-Silva J(2024)Logic-Based Explainability: Past, Present and FutureLeveraging Applications of Formal Methods, Verification and Validation. Software Engineering Methodologies10.1007/978-3-031-75387-9_12(181-204)Online publication date: 27-Oct-2024
https://dl.acm.org/doi/10.1007/978-3-031-75387-9_12
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Abdulla PLiang CRümmer P(2024)Boosting Constrained Horn Solving by Unsat Core LearningVerification, Model Checking, and Abstract Interpretation10.1007/978-3-031-50524-9_13(280-302)Online publication date: 15-Jan-2024
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Li SLi CLuo MColl JHabet DManyà FElkind E(2023)A new variable ordering for in-processing bounded variable elimination in SAT solversProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/220(1979-1987)Online publication date: 19-Aug-2023
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Nikfarjam ARothenberger RNeumann FFriedrich TSilva SPaquete L(2023)Evolutionary Diversity Optimisation in Constructing Satisfying AssignmentsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590517(938-945)Online publication date: 15-Jul-2023
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Fichte JBerre DHecher MSzeider S(2023)The Silent (R)evolution of SATCommunications of the ACM10.1145/356046966:6(64-72)Online publication date: 24-May-2023
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