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Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time

Published:16 December 2018Publication History
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Abstract

We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of basic semialgebraic sets that works in weak exponential time. That is, 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 that is doubly exponential (and this is so for almost all data).

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        cover image Journal of the ACM
        Journal of the ACM  Volume 66, Issue 1
        February 2019
        315 pages
        ISSN:0004-5411
        EISSN:1557-735X
        DOI:10.1145/3299993
        Issue’s Table of Contents

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        Publication History

        • Published: 16 December 2018
        • Accepted: 1 September 2018
        • Revised: 1 April 2018
        • Received: 1 June 2017
        Published in jacm Volume 66, Issue 1

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