Butti, SilviaDalmau, Víctor2023-01-202023-01-202022Butti S, Dalmau V. The complexity of the distributed constraint satisfaction problem. In: Bläser M, Monmege B, editors. 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021); 2021 Mar 16-19; Saarbrücken, Germany. Germany: Dagstuhl Publishing; 2021;(20):18 p. DOI: 10.4230/LIPIcs.STACS.2021.201432-4350http://hdl.handle.net/10230/55356Comunicació presentada a: STACS 2021 celebrat del 16 a 19 de març de 2021 a Saarbrücken, Alemanya.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.application/pdfeng© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.AlgorismesProgramació linealinfo:eu-repo/semantics/conferenceObjecthttp://dx.doi.org/10.1007/s00224-022-10091-yinfo:eu-repo/semantics/openAccess