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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).
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https://hal.archives-ouvertes.fr/hal-01545657
Contributor : Pierre Lairez <>
Submitted on : Wednesday, December 19, 2018 - 3:52:36 PM
Last modification on : Monday, February 24, 2020 - 3:51:04 PM
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Peter Bürgisser, Felipe Cucker, Pierre Lairez. Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time. Journal of the ACM (JACM), Association for Computing Machinery, 2018, 66 (1), pp.1-30. ⟨10.1145/3275242⟩. ⟨hal-01545657v2⟩

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