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DOI: 10.4230/LIPIcs.ESA.2018.28

Weighted Model Counting on the GPU by Exploiting Small Treewidth

Authors: Johannes K. Fichte, Markus Hecher, Stefan Woltran, and Markus Zisser

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

We propose a novel solver that efficiently finds almost the exact number of solutions of a Boolean formula (#Sat) and the weighted model count of a weighted Boolean formula (WMC) if the treewidth of the given formula is sufficiently small. The basis of our approach are dynamic programming algorithms on tree decompositions, which we engineered towards efficient parallel execution on the GPU. We provide thorough experiments and compare the runtime of our system with state-of-the-art #Sat and WMC solvers. Our results are encouraging in the sense that also complex reasoning problems can be tackled by parameterized algorithms executed on the GPU if instances have treewidth at most 30, which is the case for more than half of counting and weighted counting benchmark instances.

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Johannes K. Fichte, Markus Hecher, Stefan Woltran, and Markus Zisser. Weighted Model Counting on the GPU by Exploiting Small Treewidth. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{fichte_et_al:LIPIcs.ESA.2018.28,
  author =	{Fichte, Johannes K. and Hecher, Markus and Woltran, Stefan and Zisser, Markus},
  title =	{{Weighted Model Counting on the GPU by Exploiting Small Treewidth}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.28},
  URN =		{urn:nbn:de:0030-drops-94915},
  doi =		{10.4230/LIPIcs.ESA.2018.28},
  annote =	{Keywords: Parameterized Algorithms, Weighted Model Counting, General Purpose Computing on Graphics Processing Units, Dynamic Programming, Tree Decompositions, Treewidth}
}

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Weighted Model Counting on the GPU by Exploiting Small Treewidth

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