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.
Bibliographical noteFunding Information:
∗ Work supported in part by a grant of th e Binational Israel-US Science Foundation. † Work partially supported by grant 032-7736 from th e Israel Academy of Sciences. Part of th is work was done during a visit to th e Institute for Advanced Study, under th e support of a Sloan Foundation grant 96-6-2.