License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2021.82
URN: urn:nbn:de:0030-drops-146634
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14663/
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Wörz, Florian ; Lorenz, Jan-Hendrik

Evidence for Long-Tails in SLS Algorithms

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LIPIcs-ESA-2021-82.pdf (1 MB)

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.

BibTeX - Entry

@InProceedings{worz_et_al:LIPIcs.ESA.2021.82,
  author =	{W\"{o}rz, Florian and Lorenz, Jan-Hendrik},
  title =	{{Evidence for Long-Tails in SLS Algorithms}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{82:1--82:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14663},
  URN =		{urn:nbn:de:0030-drops-146634},
  doi =		{10.4230/LIPIcs.ESA.2021.82},
  annote =	{Keywords: Stochastic Local Search, Runtime Distribution, Statistical Analysis, Lognormal Distribution, Long-Tailed Distribution, SAT Solving}
}

Keywords: Stochastic Local Search, Runtime Distribution, Statistical Analysis, Lognormal Distribution, Long-Tailed Distribution, SAT Solving
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021
Supplementary Material: See [Florian Wörz and Jan-Hendrik Lorenz, 2021]:
Software (Base instances and modifications): https://doi.org/10.5281/zenodo.4715893
Software (Visual and statistical evaluations): https://doi.org/10.5281/zenodo.5026180

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