Method of the Multidimensional Sieve in the Practical Realization of some Combinatorial Algorithms

TL;DR

This paper presents a modified multidimensional sieve method to improve the practical implementation of combinatorial algorithms, addressing difficulties in selecting elements with specific properties in large sets.

Contribution

Introduces a new multidimensional sieve approach using arrays, with theoretical proofs for selecting representatives and calculating set cardinalities.

Findings

Effective in selecting representatives from equivalence classes

Enables calculation of factor set cardinalities

Addresses practical implementation challenges

Abstract

Some difficulties regarding the application of the well-known sieve method are considered in the case when a practical (program) realization of selecting elements, having a particular property among the elements of a set with a sufficiently great cardinal number(cardinality). In this paper the problem has been resolved by using a modified version of the method, utilizing multidimensional arrays. As a theoretical illustration of the method of the multidimensional sieve, the problem of obtaining a single representative of each equivalence class with respect to a given relation of equivalence and obtaining the cardinality of the respective factor set is considered with relevant mathematical proofs.