Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 545-568 |
| Number of pages | 24 |
| Journal | Combinatorica |
| Volume | 20 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2000 |
| Externally published | Yes |
Bibliographical note
Funding 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.