On the polyhedral decision problem

Abstract

Abstract. Computational problems sometimes can be cast in the following form: Given a point x in R, determine if x lies in some fixed polyhedron. In this paper we give a general lower bound to the complexity of such problems, showing that 1/2 log2 fs linear comparisons are needed in the worst case, for any polyhedron with fs s-dimensional faces. For polyhedra with abundant faces, this leads to lower bounds nonlinear in n, the number of variables

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