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arXiv · 2309.04601

Dyadic linear programming and extensions

Ahmad Abdi·Gérard Cornuéjols·Bertrand Guenin·Levent Tunçel
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Abstract

A rational number is dyadic if it has a finite binary representation $p/2^k$, 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.

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Ahmad Abdi, Gérard Cornuéjols, Bertrand Guenin, Levent Tunçel. 2023-09-08. Dyadic linear programming and extensions. https://arxiv.org/abs/2309.04601

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