Computing Roadmaps of General Semi-Algebraic Sets

In this paper we study the problem of determining whether two points lie in the same connected component of a semi-algebraic set S. Although we are mostly concerned with sets S⊆R k , our algorithm can also decide if points in an arbitrary set S⊆R k can be joined by a semi-algebraic path, for any real closed field R. Our algorithm computer a one-dimensional semi-algebraic subset R(S) of S (actually of an embedding of S in a space R k for a certain real extension field R of the given field R). R(S) is called the roadmap of S. The basis of this work is the eoadmap algorithm described in [3, 4] which worked only for compact, regularly stratified sets

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