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.STACS.2021.20
URN: urn:nbn:de:0030-drops-136654
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13665/
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Butti, Silvia ; Dalmau, Victor

The Complexity of the Distributed Constraint Satisfaction Problem

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LIPIcs-STACS-2021-20.pdf (0.8 MB)

Abstract

We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with each other by sending messages through fixed communication channels. Our results endorse the well-known fact from classical CSPs that the complexity of fixed-template computational problems depends on the template’s invariance under certain operations. Specifically, we show that DCSP(Γ) is polynomial-time tractable if and only if Γ is invariant under symmetric polymorphisms of all arities. Otherwise, there are no algorithms that solve DCSP(Γ) in finite time. We also show that the same condition holds for the search variant of DCSP.
Collaterally, our results unveil a feature of the processes' neighbourhood in a distributed network, its iterated degree, which plays a major role in the analysis. We explore this notion establishing a tight connection with the basic linear programming relaxation of a CSP.

BibTeX - Entry

@InProceedings{butti_et_al:LIPIcs.STACS.2021.20,
  author =	{Butti, Silvia and Dalmau, Victor},
  title =	{{The Complexity of the Distributed Constraint Satisfaction Problem}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13665},
  URN =		{urn:nbn:de:0030-drops-136654},
  doi =		{10.4230/LIPIcs.STACS.2021.20},
  annote =	{Keywords: Constraint Satisfaction Problems, Distributed Algorithms, Polymorphisms}
}

Keywords: Constraint Satisfaction Problems, Distributed Algorithms, Polymorphisms
Collection: 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Issue Date: 2021
Date of publication: 10.03.2021

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