Leitung

Prof. Dr. Peter Bürgisser

Anschrift
Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin

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Raum MA 317 (3. OG)
Institut für Mathematik

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Beate Nießen
Raum MA 318
Tel.: +49 (0)30 314 - 25771

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pbuerg@math.tu-berlin.de
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Computing the homology of basic semialgebraic sets in weak exponential time
Citation key	CBL-Computing-The-Homology-Of-Basic-Semialgebraic-Sets-In-Weak-Exponential-Time
Author	Felipe Cucker and Peter Bürgisser and Pierre Lairez
Year	2019
DOI	10.1145/3275242
Journal	Journal of the Association for Computing Machinery
Volume	66
Number	1
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).