TY - GEN
T1 - Faster Algorithm for Unique (k, 2)-CSP
AU - Zamir, Or
N1 - Publisher Copyright:
© 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
PY - 2022/9/1
Y1 - 2022/9/1
N2 - 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.
AB - 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.
KW - Algorithms
KW - Constraint Satisfaction Problem
UR - http://www.scopus.com/inward/record.url?scp=85137581856&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ESA.2022.92
DO - 10.4230/LIPIcs.ESA.2022.92
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AN - SCOPUS:85137581856
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 30th Annual European Symposium on Algorithms, ESA 2022
A2 - Chechik, Shiri
A2 - Navarro, Gonzalo
A2 - Rotenberg, Eva
A2 - Herman, Grzegorz
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 30th Annual European Symposium on Algorithms, ESA 2022
Y2 - 5 September 2022 through 9 September 2022
ER -