On the permanent of random tensors

TL;DR

This paper introduces a deterministic quasi-polynomial time algorithm and a PTAS for approximating the permanent of complex random tensors, especially when their mean module is sufficiently large, addressing a challenging computational problem.

Contribution

It presents the first deterministic quasi-polynomial time algorithm and a PTAS for approximating permanents of complex random tensors with certain mean conditions.

Findings

Algorithm achieves approximation in quasi-polynomial time.

PTAS provides near-optimal solutions for tensor permanents.

Applicable to tensors with mean module at least 1/polylog(n).

Abstract

The exact computation of permanent for high-dimensional tensors is a hard problem. Having in mind the applications of permanents in other fields, providing an algorithm for the approximation of tensor permanents is an attractive subject. In this paper, we design a deterministic quasi-polynomial time algorithm and a PTAS that computes the permanent of complex random tensors that its module of the mean is at least 1/polylog(n).