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DOI: 10.4230/LIPIcs.MFCS.2017.4

The Complexity of Boolean Surjective General-Valued CSPs

Authors: Peter Fulla and Stanislav Zivny

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract

Valued constraint satisfaction problems (VCSPs) are discrete optimisation problems with the objective function given as a sum of fixed-arity functions; the values are rational numbers or infinity. In Boolean surjective VCSPs variables take on labels from D={0,1} and an optimal assignment is required to use both labels from D. A classic example is the global min-cut problem in graphs. Building on the work of Uppman, we establish a dichotomy theorem and thus give a complete complexity classification of Boolean surjective VCSPs. The newly discovered tractable case has an interesting structure related to projections of downsets and upsets. Our work generalises the dichotomy for {0,infinity}-valued constraint languages corresponding to CSPs) obtained by Creignou and Hebrard, and the dichotomy for {0,1}-valued constraint languages (corresponding to Min-CSPs) obtained by Uppman.

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Peter Fulla and Stanislav Zivny. The Complexity of Boolean Surjective General-Valued CSPs. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{fulla_et_al:LIPIcs.MFCS.2017.4,
  author =	{Fulla, Peter and Zivny, Stanislav},
  title =	{{The Complexity of Boolean Surjective General-Valued CSPs}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.4},
  URN =		{urn:nbn:de:0030-drops-80623},
  doi =		{10.4230/LIPIcs.MFCS.2017.4},
  annote =	{Keywords: constraint satisfaction problems, surjective CSP, valued CSP, min-cut, polymorphisms, multimorphisms}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2016.39

On Planar Valued CSPs

Authors: Peter Fulla and Stanislav Zivny

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract

We study the computational complexity of planar valued constraint satisfaction problems (VCSPs). First, we show that intractable Boolean VCSPs have to be self-complementary to be tractable in the planar setting, thus extending a corresponding result of Dvorak and Kupec [ICALP'15] from CSPs to VCSPs. Second, we give a complete complexity classification of conservative planar VCSPs on arbitrary finite domains. As it turns out, in this case planarity does not lead to any new tractable cases, and thus our classification is a sharpening of the classification of conservative VCSPs by Kolmogorov and Zivny [JACM'13].

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Peter Fulla and Stanislav Zivny. On Planar Valued CSPs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 39:1-39:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{fulla_et_al:LIPIcs.MFCS.2016.39,
  author =	{Fulla, Peter and Zivny, Stanislav},
  title =	{{On Planar Valued CSPs}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{39:1--39:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.39},
  URN =		{urn:nbn:de:0030-drops-64537},
  doi =		{10.4230/LIPIcs.MFCS.2016.39},
  annote =	{Keywords: constraint satisfaction, valued constraint satisfaction, planarity, polymorphisms, multimorphisms}
}

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The Complexity of Boolean Surjective General-Valued CSPs

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On Planar Valued CSPs

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