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Some Algorithmic Problems in Polytope Theory

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arxiv math/0202204 v1 pith:4PEIJSCU submitted 2002-02-20 math.CO math.MG

Some Algorithmic Problems in Polytope Theory

classification math.CO math.MG
keywords problemsalgorithmiccombinatorialpolytopesbeyondcomplexityconvexcoordinate
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This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The problems are grouped into the sections ``Coordinate Descriptions'', ``Combinatorial Structure'', ``Isomorphism'', ``Optimization'', ``Realizability'', and ``Beyond Polytopes''.

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