Two parallel dynamic lexicographic algorithms for factorization sets in numerical semigroups

TL;DR

This paper introduces two advanced algorithms for factorization sets in numerical semigroups, enhancing existing methods with parallelization and dynamic features, and provides CUDA implementations with runtime measurements.

Contribution

It extends existing algorithms by adding lexicographic, parallel, and dynamic capabilities, and demonstrates their implementation and performance in CUDA.

Findings

Algorithms are successfully parallelized and made dynamic.

CUDA implementations show measurable runtime improvements.

New methods outperform previous static algorithms.

Abstract

To the existing dynamic algorithm FactorizationsUpToElement for factorization sets of elements in a numerical semigroup, we add lexicographic and parallel behavior. To the existing parallel lexicographic algorithm for the same, we add dynamic behavior. The (dimensionwise) dynamic algorithm is parallelized either elementwise or factorizationwise, while the parallel lexicographic algorithm is made dynamic with low-dimension tabulation. The tabulation for the parallel lexicographic algorithm can itself be performed using the dynamic algorithm. We provide reference CUDA implementations with measured runtimes.