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Beyond Boolean Surjective VCSPs

Authors: Gregor Matl and Stanislav Živný

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

Fulla, Uppman, and Živný [ACM ToCT'18] established a dichotomy theorem for Boolean surjective general-valued constraint satisfaction problems (VCSPs), i.e., VCSPs on two-element domains in which both labels have to be used in a solution. This result, in addition to identifying the complexity frontier, features the discovery of a new non-trivial tractable case (called EDS) that does not appear in the non-surjective setting. In this work, we go beyond Boolean domains. As our main result, we introduce a generalisation of EDS to arbitrary finite domains called SEDS (similar to EDS) and establish a conditional complexity classification of SEDS VCSPs based on a reduction to smaller domains. This gives a complete classification of SEDS VCSPs on three-element domains. The basis of our tractability result is a natural generalisation of the Min-Cut problem, in which only solutions of certain size (given by a lower and upper bound) are permitted. We show that all near-optimal solutions to this problem can be enumerated in polynomial time, which might be of independent interest.

Cite as

Gregor Matl and Stanislav Živný. Beyond Boolean Surjective VCSPs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 52:1-52:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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  author =	{Matl, Gregor and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Beyond Boolean Surjective VCSPs}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{52:1--52:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.52},
  URN =		{urn:nbn:de:0030-drops-102911},
  doi =		{10.4230/LIPIcs.STACS.2019.52},
  annote =	{Keywords: constraint satisfaction problems, valued constraint satisfaction, surjective constraint satisfaction, graph cuts}
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