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Hoon Hong

Department of Mathematics North Carolina State University USA


Connectivity in Semialgebraic Sets

= Symbolic and Numeric Approach=

Hoon Hong

Department of Mathematics
North Carolina State University 

Abstract. A semialgebraic set is a subset of real space defined by polynomial equations and inequalities.  A semialgebraic set  is a union of finitely many maximally connected components. In this talk, we consider the problem of deciding whether  two given points in a semialgebraic set are connected, that  is,  whether the two points lie in  a same connected  component. In particular, we consider the semialgebraic set defined by f not equal 0 where f is a given bivariate  polynomial. The  motivation comes from the observation that many  important/non-trivial  problems in science and engineering  can be often reduced to that of connectivity. Due to it  importance, there has been intense research effort on the  problem. We will describe a method based on gradient fields and  provide a sketch of the proof of correctness based Morse  complex.  The method seems to be more efficient  than the previous methods in practice.


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