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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. ORCID: 0000-0003-4935-7820 (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 Berlin / Heidelberg, pp. 382-395. ISBN 9783540407706

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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:
Additional Information: © 2003 Springer Verlag Berlin Heidelberg
Divisions: Management
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited: 13 May 2011 12:46
Last Modified: 16 May 2024 04:53

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