DeepAI AI Chat
Log In Sign Up

Linear Programming using Limited-Precision Oracles

12/30/2019
by   Ambros Gleixner, et al.
0

Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations necessary, or the cost of all arithmetic operations is considered through a bit-complexity analysis. Yet in practice, implementations typically use limited-precision arithmetic. In this paper we introduce the idea of a limited-precision LP oracle and study how such an oracle could be used within a larger framework to compute exact precision solutions to LPs. Under mild assumptions, it is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. This work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly.

READ FULL TEXT

page 1

page 2

page 3

page 4

09/10/2020

Revisiting Tardos's Framework for Linear Programming: Faster Exact Solutions using Approximate Solvers

In breakthrough work, Tardos (Oper. Res. '86) gave a proximity based fra...
07/08/2019

Solving p-adic polynomial systems via iterative eigenvector algorithms

In this article, we describe an implementation of a polynomial system so...
12/12/2019

A scaling-invariant algorithm for linear programming whose running time depends only on the constraint matrix

Following the breakthrough work of Tardos in the bit-complexity model, V...
02/18/2019

A Quantum IP Predictor-Corrector Algorithm for Linear Programming

We introduce a new quantum optimization algorithm for Linear Programming...
01/29/2021

lrsarith: a small fixed/hybrid arithmetic C library

We describe lrsarith which is a small fixed precision and hybrid arithme...
11/05/2018

Complexity Estimates for Fourier-Motzkin Elimination

In this paper, we propose a new method for removing all the redundant in...
03/05/2022

On the Error of Random Sampling: Uniformly Distributed Random Points on Parametric Curves

Given a parametric polynomial curve γ:[a,b]→ℝ^n, how can we sample a ran...