A New Fast Computation of a Permanent

TL;DR

This paper introduces Store-zechin, a novel recursive algorithm that leverages storage and multiplexing to compute matrix permanents more efficiently than existing methods, promising improved computational prospects.

Contribution

The paper presents Store-zechin, a new recursive algorithm that significantly reduces the number of operations needed to compute a matrix permanent compared to Ryser and R-N-W algorithms.

Findings

Store-zechin requires fewer multiplications and additions than Ryser and R-N-W algorithms.

The algorithm effectively utilizes memory to avoid redundant calculations.

Store-zechin shows better application prospects due to its efficiency.

Abstract

This paper proposes a general algorithm called Store-zechin for quickly computing the permanent of an arbitrary square matrix. Its key idea is storage, multiplexing, and recursion. That is, in a recursive process, some sub-terms which have already been calculated are no longer calculated, but are directly substituted with the previous calculation results. The new algorithm utilizes sufficiently computer memories and stored data to speed the computation of a permanent. The Analyses show that computating the permanent of an n * n matrix by Store-zechin requires (2^(n - 1)- 1)n multiplications and (2^(n-1))(n - 2)+ 1 additions while does (2^n - 1)n + 1 multiplications and (2^n - n)(n + 1)- 2 additions by the Ryser algorithm, and does (2^(n - 1))n + (n + 2) multiplications and (2^(n - 1))(n + 1)+ (n^2 - n -1) additions by the R-N-W algorithm. Therefore, Store-zechin is excellent more than the latter two algorithms, and has a better application prospect.