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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).
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