Dyadic linear programming and extensions

Abdi, Ahmad ORCID: 0000-0002-3008-4167, Cornuéjols, Gérard, Guenin, Bertrand and Tunçel, Levent (2024) Dyadic linear programming and extensions. Mathematical Programming. ISSN 0025-5610

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Abstract

A rational number is dyadic if it has a finite binary representation p/2k, where p is an integer and k is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in floating-point arithmetic on a computer. A vector is dyadic if all its entries are dyadic rationals. We study the problem of finding a dyadic optimal solution to a linear program, if one exists. We show how to solve dyadic linear programs in polynomial time. We give bounds on the size of the support of a solution as well as on the size of the denominators. We identify properties that make the solution of dyadic linear programs possible: closure under addition and negation, and density, and we extend the algorithmic framework beyond the dyadic case.

Item Type:	Article
Official URL:	https://link.springer.com/journal/10107
Additional Information:	© 2024 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	14 Oct 2024 07:03
Last Modified:	23 Oct 2024 09:57
URI:	http://eprints.lse.ac.uk/id/eprint/125702

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