An improved algorithm to compute the $\omega$-primality

TL;DR

This paper introduces an enhanced algorithm for calculating the $\, ext{omega}$-primality of numerical semigroups, leveraging advanced optimization techniques to improve computational efficiency over previous methods.

Contribution

The paper presents a novel approach that adapts recent resolution methods for linear programming to efficiently compute the $\, ext{omega}$-invariant, advancing the state of the art.

Findings

The proposed method outperforms existing algorithms in computational experiments.

The new approach effectively optimizes linear functions over efficient solutions.

Numerical results demonstrate improved speed and accuracy.

Abstract

In this paper, we present an improved methodology to compute $\omega$-invariant of numerical semigroup. The approach is based on adapting a recent resolution method for optimizing a linear function over the set of efficient solutions of a multiple objective integer linear programming problem. The numerical experiments show the efficiency of the proposed technique compared to the existing methods.