On Improving the Backjump Level in PB Solvers

by   Romain Wallon, et al.

Current PB solvers implement many techniques inspired by the CDCL architecture of modern SAT solvers, so as to benefit from its practical efficiency. However, they also need to deal with the fact that many of the properties leveraged by this architecture are no longer true when considering PB constraints. In this paper, we focus on one of these properties, namely the optimality of the so-called first unique implication point (1-UIP). While it is well known that learning the first assertive clause produced during conflict analysis ensures to perform the highest possible backjump in a SAT solver, we show that there is no such guarantee in the presence of PB constraints. We also introduce and evaluate different approaches designed to improve the backjump level identified during conflict analysis by allowing to continue the analysis after reaching the 1-UIP. Our experiments show that sub-optimal backjumps are fairly common in PB solvers, even though their impact on the solver is not clear.


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0.1 Introduction

0.2 Preliminaries

0.3 Sub-Optimal Backjumps in PB Solvers

0.4 Towards an Improvement of the Backjump Level

0.5 Experimental Results

0.6 Conclusion


The author is grateful to the anonymous reviewers for their numerous comments, that greatly helped to improve the paper. The author is also grateful to the CRIL laboratory (CNRS UMR 8188, Université d’Artois) for having supplied the computational resources on which the experiments presented in this paper have been run. This publication was supported by the Chair “Integrated Urban Mobility”, backed by L’X – École Polytechnique and La Fondation de l’École Polytechnique and sponsored by Uber. The Partners of the Chair shall not under any circumstances accept any liability for the content of this publication, for which the author shall be solely liable.