Section: New Results

Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time

In [9], Pierre Lairez, jointly with Peter Bürgisser (TU Berlin) and Felipe Cucker (City University of Hong Kong), has described and analyzed an algorithm for computing the homology (Betti numbers and torsion coefficients) of basic semialgebraic sets. The algorithm 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 that is doubly exponential (and this is so for almost all data).