Approximating the Permanent in O∗(n7) Time
نویسندگان
چکیده
The first polynomial-time algorithm to approximate (with arbitrary precision) the permanent of a non-negative matrix was presented by Jerrum, Sinclair and Vigoda. They designed a simulated annealing algorithm with a running time of O∗(n26) for 0/1 matrices. Subsequently, they improved their analysis, resulting in a O∗(n10) time algorithm. We present a O∗(n7) time algorithm. Our improvement comes from an improved “cooling schedule” for the simulated annealing algorithm, and a refined analysis of the underlying Markov chain.
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