Erschienen in:

1997 | OriginalPaper | Buchkapitel

Computing Roadmaps of Semi-algebraic Sets on a Variety (Extended Abstract)

verfasst von : Saugata Basu, Richard Pollack, Marie-Françoise Roy

Erschienen in: Foundations of Computational Mathematics

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

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We consider a semi-algebraic set S defined by s polynomials of degree at most d in k variables contained in an algebraic variety V of dimension k’ defined as the zero set of a polynomial of degree d and two points defined by polynomials of degree t. We present an algorithm for computing a semi-algebraic path in S connecting two points if they happen to lie in the same connected component of S which works in time $$({s^{k' + 1}} + k's{t^{0(1)}}){d^{O({k^2})}}$$.

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