Single exponential path finding in semialgebraic sets Part I: The case of a regular bounded hypersurface

  • Joos Heintz
  • Marie-Francoise Roy
  • Pablo Solernó
Submitted Contributions Computational Algebra And Geometry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 508)


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.


Transfer Principle Parallel Complexity Real Closed Field Semialgebraic Subset Quantifier Free Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Joos Heintz
    • 2
    • 3
  • Marie-Francoise Roy
    • 1
  • Pablo Solernó
    • 2
    • 3
  1. 1.IRMAR. Université de Rennes IRennes CedexFrance
  2. 2.Working Group Noaï Fitchas. Instituto Argentino de Matemática CONICETBuenos AiresArgentina
  3. 3.Facultad de Ciencias Exactas y Naturales. Dpto. de Matemática (Univ. de Buenos Aires)Ciudad UniversitariaArgentina

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