On an application of multidimensional arrays

TL;DR

This paper explores how multidimensional arrays can be used to implement combinatorial algorithms efficiently, demonstrated through a problem in binary matrices relevant to textile industry modeling.

Contribution

It introduces a method utilizing multidimensional arrays to solve combinatorial problems involving large sets and equivalence classes.

Findings

Efficient enumeration of representatives from equivalence classes.

Application of the method to binary matrices in textile modeling.

Addresses implementation difficulties in combinatorial algorithms.

Abstract

This article discusses some difficulties in the implementation of combinatorial algorithms associated with the choice of all elements with certain properties among the elements of a set with great cardinality.The problem has been resolved by using multidimensional arrays. Illustration of the method is a solution of the problem of obtaining one representative from each equivalence class with respect to the described in the article equivalence relation in the set of all $m\sim n$ binary matrices. This equivalence relation has an application in the mathematical modeling in the textile industry.