Computing the permanent of (some) complex matrices
Combinatorics
2014-06-25 v2 Data Structures and Algorithms
Mathematical Physics
math.MP
Optimization and Control
Abstract
We present a deterministic algorithm, which, for any given 0< epsilon < 1 and an nxn real or complex matrix A=(a_{ij}) such that | a_{ij}-1| < 0.19 for all i, j computes the permanent of A within relative error epsilon in n^{O(ln n -ln epsilon)} time. The method can be extended to computing hafnians and multidimensional permanents.
Cite
@article{arxiv.1405.1303,
title = {Computing the permanent of (some) complex matrices},
author = {Alexander Barvinok},
journal= {arXiv preprint arXiv:1405.1303},
year = {2014}
}
Comments
12 pages, results extended to hafnians and multidimensional permanents, minor improvements