2026-07-21T23:35:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13665 2024-03-06T10:52:36Z ddc:004 open_access

The Complexity of the Distributed Constraint Satisfaction Problem Butti, Silvia Dalmau, Victor Constraint Satisfaction Problems Distributed Algorithms Polymorphisms 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Silvia Butti and Victor Dalmau 2021 Is Part Of LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2021.20 urn:nbn:de:0030-drops-136654 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.20 eng https://creativecommons.org/licenses/by/4.0/legalcode