A Deterministic Strongly Polynomial Algorithm for Matrix Scaling and Approximate Permanents

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. 1 

• Type: Conference
• Year: 1998
• Where: STOC
• Authors: Nathan Linial, Alex Samorodnitsky, Avi Wigderson
• Keywords: Algorithm, Algorithms, Hebrew University, Polynomial Algorithm, STOC 1998