Exact 2-CSP Optimization Using Matrix Multiplication
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Microsoft Research330 тыс
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Опубликовано 6 сентября 2016, 21:25
We investigate the complexity of exactly solving NP-hard optimization problems involving at most two variables per constraint, such as MAX-CUT, MAX-2-SAT, and MIN-BISECTION. For years it was not known if one could solve such problems in time significantly less than 2^n (trying all possible assignments). WeΓÇÖll present an algorithm that reduces any 2-CSP optimization problem to a (very, very large) matrix multiplication problem. Let n^{omega} be the runtime of some matrix multiplication algorithm M on n by n matrices (note omega < 2.4 for some M). Using that M, the algorithm for 2-CSP optimization will run in 2^{omega n/3} time, modulo polynomial factors.
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