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An Efficient Parametric Linear Programming Solver and Application to Polyhedral Projection (1911.09755v1)
Published 18 Nov 2019 in math.OC, cs.CG, and cs.PL
Abstract: Polyhedral projection is a main operation of the polyhedron abstract domain.It can be computed via parametric linear programming (PLP), which is more efficient than the classic Fourier-Motzkin elimination method.In prior work, PLP was done in arbitrary precision rational arithmetic.In this paper, we present an approach where most of the computation is performed in floating-point arithmetic, then exact rational results are reconstructed.We also propose a workaround for a difficulty that plagued previous attempts at using PLP for computations on polyhedra: in general the linear programming problems are degenerate, resulting in redundant computations and geometric descriptions.