Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of the ACM (JACM) Year : 2018

Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time

Abstract

We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of basic semialgebraic sets which works in weak exponential time. That is, out of a set of exponentially small measure in the space of data the cost of the algorithm is exponential in the size of the data. All algorithms previously proposed for this problem have a complexity which is doubly exponential (and this is so for almost all data).
Fichier principal
Vignette du fichier
Semialgebraic.pdf (892.9 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01545657 , version 1 (22-06-2017)
hal-01545657 , version 2 (19-12-2018)

Identifiers

Cite

Peter Bürgisser, Felipe Cucker, Pierre Lairez. Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time. Journal of the ACM (JACM), 2018, 66 (1), pp.1-30. ⟨10.1145/3275242⟩. ⟨hal-01545657v2⟩
294 View
218 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More