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Approximation Strategies for Incomplete MaxSAT

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Principles and Practice of Constraint Programming (CP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11008))

Abstract

Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of the unsatisfied soft clauses without providing any optimality guarantees. In this paper, we propose two approximation strategies for improving incomplete MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. Experimental results show that approximation strategies can be used to find better solutions than the best incomplete solvers in the MaxSAT Evaluation 2017.

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Notes

  1. 1.

    For simplicity, we will assume that \(\varphi _h\) is always satisfiable.

  2. 2.

    \(best(\varphi )\) is the cost of the best solution found by any solver in this evaluation.

  3. 3.

    We consider a score of 0 if \(\mathcal S\) did not find any solution to \(\varphi \).

  4. 4.

    Even though MaxHS [11] placed first in the complete weighted category of the MSE2017, its incomplete version is not as competitive as the other solvers [2].

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Acknowledgements

This work is partially funded by ECR 2017 grant from SERB, DST, India, NSF award #1762363 and CMU/AIR/0022/2017 grant. Authors would like to thank the anonymous reviewers for their helpful comments, and Saketha Nath for lending his servers for the experiments.

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Authors and Affiliations

  1. Indian Institute of Technology Hyderabad, Sangareddy, India

    Saurabh Joshi, Prateek Kumar & Sukrut Rao

  2. Carnegie Mellon University, Pittsburgh, USA

    Ruben Martins

Authors
  1. Saurabh Joshi
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  2. Prateek Kumar
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  3. Ruben Martins
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  4. Sukrut Rao
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Correspondence to Saurabh Joshi .

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Editors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    John Hooker

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Joshi, S., Kumar, P., Martins, R., Rao, S. (2018). Approximation Strategies for Incomplete MaxSAT. In: Hooker, J. (eds) Principles and Practice of Constraint Programming. CP 2018. Lecture Notes in Computer Science(), vol 11008. Springer, Cham. https://doi.org/10.1007/978-3-319-98334-9_15

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  • DOI: https://doi.org/10.1007/978-3-319-98334-9_15

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