Evidence for Long-Tails in SLS Algorithms

Authors Florian Wörz , Jan-Hendrik Lorenz



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Florian Wörz
  • Institut für Theoretische Informatik, Universität Ulm, Germany
Jan-Hendrik Lorenz
  • Institut für Theoretische Informatik, Universität Ulm, Germany

Acknowledgements

The authors acknowledge support by the state of Baden-Württemberg through bwHPC.

Cite AsGet BibTex

Florian Wörz and Jan-Hendrik Lorenz. Evidence for Long-Tails in SLS Algorithms. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 82:1-82:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ESA.2021.82

Abstract

Stochastic local search (SLS) is a successful paradigm for solving the satisfiability problem of propositional logic. A recent development in this area involves solving not the original instance, but a modified, yet logically equivalent one [Jan{-}Hendrik Lorenz and Florian Wörz, 2020]. Empirically, this technique was found to be promising as it improves the performance of state-of-the-art SLS solvers. Currently, there is only a shallow understanding of how this modification technique affects the runtimes of SLS solvers. Thus, we model this modification process and conduct an empirical analysis of the hardness of logically equivalent formulas. Our results are twofold. First, if the modification process is treated as a random process, a lognormal distribution perfectly characterizes the hardness; implying that the hardness is long-tailed. This means that the modification technique can be further improved by implementing an additional restart mechanism. Thus, as a second contribution, we theoretically prove that all algorithms exhibiting this long-tail property can be further improved by restarts. Consequently, all SAT solvers employing this modification technique can be enhanced.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Probabilistic algorithms
  • Mathematics of computing → Distribution functions
Keywords
  • Stochastic Local Search
  • Runtime Distribution
  • Statistical Analysis
  • Lognormal Distribution
  • Long-Tailed Distribution
  • SAT Solving

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