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Impatient PPSZ - A Faster Algorithm for CSP

Authors Shibo Li , Dominik Scheder



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Shibo Li
  • Shanghai Jiao Tong University, China
Dominik Scheder
  • Shanghai Jiao Tong University, China

Acknowledgements

Dominik Scheder wants to thank Timon Hertli, Isabelle Hurbain, Sebastian Millius, Robin A. Moser, and May Szedlák, his co-authors of [Hertli et al., 2016]. The idea of impatient assignment came up when we were working on [Hertli et al., 2016].

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Shibo Li and Dominik Scheder. Impatient PPSZ - A Faster Algorithm for CSP. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 33:1-33:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ISAAC.2021.33

Abstract

PPSZ is the fastest known algorithm for (d,k)-CSP problems, for most values of d and k. It goes through the variables in random order and sets each variable randomly to one of the d colors, excluding those colors that can be ruled out by looking at few constraints at a time. We propose and analyze a modification of PPSZ: whenever all but 2 colors can be ruled out for some variable, immediately set that variable randomly to one of the remaining colors. We show that our new "impatient PPSZ" outperforms PPSZ exponentially for all k and all d ≥ 3 on formulas with a unique satisfying assignment.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Randomized algorithms
  • Constraint Satisfaction Problems
  • exponential-time algorithms

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References

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