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We present a deterministic strongly polynomial algorithm that computes the permanent of a nonnegative n × n matrix to within a multiplicative factor of en. To this end we develop the first strongly polynomial-time algorithm for matrix scaling an important nonlinear optimization problem with many applications. Our work suggests a simple new (slow) polynomial time decision algorithm for bipartite perfect matching, conceptually different from classical approaches. ∗Hebrew University. Work supported in part by a grant of the Binational Israel-US Science Foundation. †Hebrew University ‡Hebrew University. Work partially supported by grant 032-7736 from the Israel Academy of Sciences. Part of this work was done during a visit to the Institute for Advanced Study, under the support of a Sloan Foundation grant 96-6-2.

A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents