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International Conference on Principles and Practice of Constraint Programming

CP 2017: Principles and Practice of Constraint Programming pp 641–651Cite as

Reduced Cost Fixing in MaxSAT

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10416))

Abstract

We investigate utilizing the integer programming (IP) technique of reduced cost fixing to improve maximum satisfiability (MaxSAT) solving. In particular, we show how reduced cost fixing can be used within the implicit hitting set approach (IHS) for solving MaxSAT. Solvers based on IHS have proved to be quite effective for MaxSAT, especially on problems with a variety of clause weights. The unique feature of IHS solvers is that they utilize both SAT and IP techniques. We show how reduced cost fixing can be used in this framework to conclude that some soft clauses can be left falsified or forced to be satisfied without influencing the optimal cost. Applying these forcings simplifies the remaining problem. We provide an extensive empirical study showing that reduced cost fixing employed in this manner can be useful in improving the state-of-the-art in MaxSAT solving especially on hard instances arising from real-world application domains.

Work supported in part by Academy of Finland (grants 251170 COIN, 276412, 284591 and 295673), the Research Funds and DoCS Doctoral School in Computer Science of the University of Helsinki, and the Natural Sciences and Engineering Research Council of Canada.

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Notes

  1. 1.

    The variables in the LP solution are either basic or non-basic. All of the non-basic variables will be at their upper or lower bounds in the LP solution [5].

  2. 2.

    In a hitting set problem \(b_i=1\) is always feasible. However, MaxHS can also add other constraints to the hitting set problem via a process of constraint seeding [9]. It is not difficult to show that all of our results continue to hold with seeding.

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Authors and Affiliations

  1. Department of Computer Science, University of Toronto, Toronto, Canada

    Fahiem Bacchus

  2. HIIT, Department of Computer Science, University of Helsinki, Helsinki, Finland

    Antti Hyttinen, Matti Järvisalo & Paul Saikko

Authors
  1. Fahiem Bacchus
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  2. Antti Hyttinen
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  3. Matti Järvisalo
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  4. Paul Saikko
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Correspondence to Fahiem Bacchus .

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Editors and Affiliations

  1. University of Toronto, Toronto, Ontario, Canada

    J. Christopher Beck

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Bacchus, F., Hyttinen, A., Järvisalo, M., Saikko, P. (2017). Reduced Cost Fixing in MaxSAT. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham. https://doi.org/10.1007/978-3-319-66158-2_41

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  • DOI: https://doi.org/10.1007/978-3-319-66158-2_41

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