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Separate, Measure and Conquer: faster polynomial-space algorithms for Max 2-CSP and counting dominating sets

Gaspers, Serge and Sorkin, Gregory B. (2015) Separate, Measure and Conquer: faster polynomial-space algorithms for Max 2-CSP and counting dominating sets. In: Halldórsson, Magnús M. and Iwama, Kazuo and Kobayashi, Naoki and Speckmann, Bettina, (eds.) Automata, Languages, and Programming: 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part I. Lecture Notes in Computer Science,9134. Springer, pp. 567-579. ISBN 9783662476710

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Identification Number: 10.1007/978-3-662-47672-7_46

Abstract

We show a method resulting in the improvement of several polynomial-space, exponential-time algorithms. The method capitalizes on the existence of small balanced separators for sparse graphs, which can be exploited for branching to disconnect an instance into independent components. For this algorithm design paradigm, the challenge to date has been to obtain improvements in worst-case analyses of algorithms, compared with algorithms that are analyzed with advanced methods, such as Measure and Conquer. Our contribution is the design of a general method to integrate the advantage from the separator-branching into Measure and Conquer, for an improved running time analysis. We illustrate the method with improved algorithms for Max (r,2) -CSP and #Dominating Set. For Max (r,2) -CSP instances with domain size r and m constraints, the running time improves from r m/6 to r m/7.5 for cubic instances and from r 0.19⋅m to r 0.18⋅m for general instances, omitting subexponential factors. For #Dominating Set instances with n vertices, the running time improves from 1.4143 n to 1.2458 n for cubic instances and from 1.5673 n to 1.5183 n for general instances. It is likely that other algorithms relying on local transformations can be improved using our method, which exploits a non-local property of graphs.

Item Type: Book Section
Official URL: http://www.springer.com/computer/lncs?SGWID=0-164-...
Additional Information: © 2015 Springer-Verlag Berlin Heidelberg
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Sets: Departments > Mathematics
Date Deposited: 19 Jan 2016 14:25
Last Modified: 04 Apr 2017 10:15
URI: http://eprints.lse.ac.uk/id/eprint/65060

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