Sharp bound on the support of integer linear optimal solutions
Sharp bound on the support of integer linear optimal solutions
We study the support of optimal solutions of integer linear programs (ILP) that are of the form $\{\min~c^T x, ~s.t.~ Ax = b,~ x \in \Z^n_{+}\}$. We provide an upper bound on the size of the support as $(m-1)+\ceil{\log_2(g^{-1} \sqrt{det(AA^T)})}$ and show that the bound is tight in the following senses. First, we provide a class of problem where equality hold. Second, we provide a variation of \citet{aliev2018support} asymtotic lower bound of the size of the support that matches the form of the upper bound better.
University of Southampton
Nguyen, Tri-Dung
a6aa7081-6bf7-488a-b72f-510328958a8e
Nguyen, Tri-Dung
a6aa7081-6bf7-488a-b72f-510328958a8e
Nguyen, Tri-Dung
(2018)
Sharp bound on the support of integer linear optimal solutions
University of Southampton
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Monograph
(Working Paper)
Abstract
We study the support of optimal solutions of integer linear programs (ILP) that are of the form $\{\min~c^T x, ~s.t.~ Ax = b,~ x \in \Z^n_{+}\}$. We provide an upper bound on the size of the support as $(m-1)+\ceil{\log_2(g^{-1} \sqrt{det(AA^T)})}$ and show that the bound is tight in the following senses. First, we provide a class of problem where equality hold. Second, we provide a variation of \citet{aliev2018support} asymtotic lower bound of the size of the support that matches the form of the upper bound better.
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In preparation date: 2018
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Local EPrints ID: 426472
URI: http://eprints.soton.ac.uk/id/eprint/426472
PURE UUID: d20e37c2-43d1-46fa-9c60-86cc51e870e3
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Date deposited: 28 Nov 2018 17:30
Last modified: 23 Feb 2023 02:56
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Author:
Tri-Dung Nguyen
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