Sparsity Preserving Algorithms for Octagons

TL;DR

This paper introduces new algorithms for octagon analysis that maintain sparsity, improving efficiency for sparse inputs while ensuring the same level of precision as existing methods.

Contribution

The paper presents sparsity-preserving algorithms for octagons using weakly closed difference bound matrices, enhancing performance on sparse data without losing accuracy.

Findings

Algorithms preserve input sparsity and are more efficient on sparse data.

Maintains the same precision as existing algorithms.

Improves computational complexity for sparse cases.

Abstract

Known algorithms for manipulating octagons do not preserve their sparsity, leading typically to quadratic or cubic time and space complexities even if no relation among variables is known when they are all bounded. In this paper, we present new algorithms, which use and return octagons represented as weakly closed difference bound matrices, preserve the sparsity of their input and have better performance in the case their inputs are sparse. We prove that these algorithms are as precise as the known ones.