Algorithms for finding connected separators between antipodal points |
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Authors: | Jan P Boroński |
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Institution: | a Department of Mathematics and Statistics, Auburn University, Alabama 36849, USA b Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyn`ski University, ul. Dewajtis 5, 01-815 Warszawa, Poland |
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Abstract: | A set (or a collection of sets) contained in the Euclidean space Rm is symmetric if it is invariant under the antipodal map. Given a symmetric unicoherent polyhedron X (like an n-dimensional cube or a sphere) and an odd real function f defined on vertices of a certain symmetric triangulation of X, we algorithmically construct a connected symmetric separator of X by choosing a subcollection of the triangulation. Each element of the subcollection contains the vertices v and u such that f(v)f(u)?0. |
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Keywords: | primary 54H25 54-04 secondary 55M20 54F55 52B15 |
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