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Faster algorithms for MAX CUT and MAX CSP, with polynomial expected time for sparse instances

Scott, Alexander D. and Sorkin, Gregory B. (2003) Faster algorithms for MAX CUT and MAX CSP, with polynomial expected time for sparse instances. In: Arora, S., Jansen, K., Rolim, J.D.P. and Sahai, A., (eds.) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. 6th International Workshop on Approxima. Lecture notes in computer science(2764). Springer, pp. 382-395. ISBN 9783540407706

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Abstract

We show that a random instance of a weighted maximum constraint satisfaction problem (or max 2-csp), whose clauses are over pairs of binary variables, is solvable by a deterministic algorithm in polynomial expected time, in the “sparse” regime where the expected number of clauses is half the number of variables. In particular, a maximum cut in a random graph with edge density 1/n or less can be found in polynomial expected time. Our method is to show, first, that if a max 2-csp has a connected underlying graph with n vertices and m edges, the solution time can be deterministically bounded by 2(m − n)/2. Then, analyzing the tails of the distribution of this quantity for a component of a random graph yields our result. An alternative deterministic bound on the solution time, as 2 m/5, improves upon a series of recent results.

Item Type: Book Section
Official URL: http://www.springer.com
Additional Information: © 2003 Springer Verlag Berlin Heidelberg
Library of Congress subject classification: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Sets: Research centres and groups > Management Science Group
Departments > Management
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 13 May 2011 12:46
URL: http://eprints.lse.ac.uk/35818/

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