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

## 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 |
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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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