Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, September 07, 2006, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Gregory B. Sorkin (IBM T.J. Watson Research Center)

Faster solving, counting, and sampling

The class Max 2-CSP includes Max Cut, Max 2-Sat, and weighted versions of more general problems. Most exact (exponential-time) algorithms have been targeted to specific problems in the class, for example solving Max Cut in time Otilde(2^{m/4}), where m is the number of edges (constraints, generally). I will show a simple algorithm which solves any Max 2-CSP in time Otilde(2^{19m/100}), making it the fastest known algorithm even for most Max 2-CSP special cases (with exceptions such as Maximum Independent Set). For random constraint graphs up to the giant-component threshold, the algorithm runs in expected linear time, an interesting result in the context of the experimentally observed phase transition in the hardness of solving random 3-Sat instances.

The talk will focus on a new problem class, Generalized Max 2-CSP, whose partition functions may be calculated by essentially the same algorithm but whose interest transcends the algorithm. It enables us, in the same time bound Otilde(2^{19m/100}), to solve counting problems like #Max 2-Sat, to sample maximizing solutions uniformly at random (or to sample over all solutions from other distributions, such as the Gibbs distribution), and to solve problems like Max Bisection and Max Clique which do not quite fit the Max 2-CSP paradigm.

Joint work with Alexander Scott (Oxford).

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