Parallel Polynomial Permanent Mod Powers of 2 and Shortest Disjoint Cycles
Computational Complexity
2021-06-03 v1
Abstract
We present a parallel algorithm for permanent mod 2^k of a matrix of univariate integer polynomials. It places the problem in ParityL subset of NC^2. This extends the techniques of [Valiant], [Braverman, Kulkarni, Roy] and [Bj\"orklund, Husfeldt], and yields a (randomized) parallel algorithm for shortest 2-disjoint paths improving upon the recent result from (randomized) polynomial time. We also recognize the disjoint paths problem as a special case of finding disjoint cycles, and present (randomized) parallel algorithms for finding a shortest cycle and shortest 2-disjoint cycles passing through any given fixed number of vertices or edges.
Cite
@article{arxiv.2106.00714,
title = {Parallel Polynomial Permanent Mod Powers of 2 and Shortest Disjoint Cycles},
author = {Samir Datta and Kishlaya Jaiswal},
journal= {arXiv preprint arXiv:2106.00714},
year = {2021}
}