Sparsity Preserving Algorithms for Octagons

Jourdan, Jacques-Henri

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Sparsity Preserving Algorithms for Octagons

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Jourdan, Jacques-Henri
Group D. Dreyer, Max Planck Institute for Software Systems, Max Planck Society;

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arXiv:1612.00277.pdf
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Jourdan, J.-H. (2016). Sparsity Preserving Algorithms for Octagons. Retrieved from http://arxiv.org/abs/1612.00277.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-21D6-C

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.