An Efficient Parametric Linear Programming Solver and Application to Polyhedral Projection

TL;DR

This paper introduces an efficient parametric linear programming method that primarily uses floating-point arithmetic with rational reconstruction, improving the computation of polyhedral projections over traditional methods.

Contribution

It presents a novel approach combining floating-point computation with rational reconstruction and addresses degeneracy issues in polyhedral computations.

Findings

Significantly faster polyhedral projection computations.

Reduced computational redundancy in polyhedral analysis.

Effective handling of degeneracy in linear programming problems.

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.