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2005
ACM

Computing the first Betti number and the connected components of semi-algebraic sets

14 years 3 months ago
Computing the first Betti number and the connected components of semi-algebraic sets
In this paper we describe the first singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. We also describe algorithms for obtaining semi-algebraic descriptions of the semi-algebraically connected components of any given real algebraic or semi-algebraic set. Singly exponential algorithms for computing the zero-th Betti number, and the Euler-Poincar?e characteristic, were known before. No singly exponential algorithm was known for computing any of the individual Betti numbers other than the zero-th one.
Saugata Basu, Richard Pollack, Marie-Franço
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2005
Where STOC
Authors Saugata Basu, Richard Pollack, Marie-Françoise Roy
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