Abstract
Let V be a bounded semialgebraic hypersurface defined by a regular polynomial equation and let x1, x 2 be two points of V. Assume that x 1 , x 2 are given by a boolean combination of polynomial inequalities. We describe an algorithm which decides in single exponential sequential time and polynomial parallel time whether x 1 and x 2 are contained in the same semialgebraically connected component of V. If they do, the algorithm constructs a continuous semialgebraic path of V connecting x 1 and x 2 . By the way the algorithm constructs a roadmap of V. In particular we obtain that the number of semialgebraically connected components of V is computable within the mentioned time bounds.
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© 1991 Springer-Verlag Berlin Heidelberg
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Heintz, J., Roy, MF., Solernó, P. (1991). Single exponential path finding in semialgebraic sets Part I: The case of a regular bounded hypersurface. In: Sakata, S. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1990. Lecture Notes in Computer Science, vol 508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54195-0_50
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DOI: https://doi.org/10.1007/3-540-54195-0_50
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