Faster Algorithm for Unique (k, 2)-CSP

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Abstract

In a (k, 2)-Constraint Satisfaction Problem we are given a set of arbitrary constraints on pairs of k-ary variables, and are asked to find an assignment of values to these variables such that all constraints are satisfied. The (k, 2)-CSP problem generalizes problems like k-coloring and k-list-coloring. In the Unique (k, 2)-CSP problem, we add the assumption that the input set of constraints has at most one satisfying assignment. Beigel and Eppstein gave an algorithm for (k, 2)-CSP running in time O ((0.4518k)n) for k > 3 and O (1.356n) for k = 3, where n is the number of variables. Feder and Motwani improved upon the Beigel-Eppstein algorithm for k ≥ 11. Hertli, Hurbain, Millius, Moser, Scheder and Szedlák improved these bounds for Unique (k, 2)-CSP for every k ≥ 5. We improve the result of Hertli et al. and obtain better bounds for Unique (k, 2)-CSP for k ≥ 5. In particular, we improve the running time of Unique (5, 2)-CSP from O (2.254n) to O (2.232n) and Unique (6, 2)-CSP from O (2.652n) to O (2.641n). Recently, Li and Scheder also published an improvement over the algorithm of Hertli et al. in the same regime as ours. Their improvement does not include quantitative bounds, we compare the works in the paper.

Original languageEnglish
Title of host publication30th Annual European Symposium on Algorithms, ESA 2022
EditorsShiri Chechik, Gonzalo Navarro, Eva Rotenberg, Grzegorz Herman
ISBN (Electronic)9783959772471
DOIs
StatePublished - 1 Sep 2022
Externally publishedYes
Event30th Annual European Symposium on Algorithms, ESA 2022 - Berlin/Potsdam, Germany
Duration: 5 Sep 20229 Sep 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume244

Conference

Conference30th Annual European Symposium on Algorithms, ESA 2022
Country/TerritoryGermany
CityBerlin/Potsdam
Period5/09/229/09/22

Keywords

  • Algorithms
  • Constraint Satisfaction Problem

All Science Journal Classification (ASJC) codes

  • Software

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