The support of integer optimal solutions

Aliev, I. ORCID: https://orcid.org/0000-0002-2206-9207, De Loera, J. A., Eisenbrand, F., Oertel, T. ORCID: https://orcid.org/0000-0001-5720-8978 and Weismantel, R. 2018. The support of integer optimal solutions. SIAM Journal on Optimization 28 (3) , pp. 2152-2157. 10.1137/17M1162792

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Abstract

The support of a vector is the number of nonzero-components. We show that given an integral m×n matrix A, the integer linear optimization problem max{cTx:Ax=b,x≥0,x∈Zn} has an optimal solution whose support is bounded by 2mlog(2m−−√∥A∥∞), where ∥A∥∞ is the largest absolute value of an entry of A. Compared to previous bounds, the one presented here is independent on the objective function. We furthermore provide a nearly matching asymptotic lower bound on the support of optimal solutions.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	1052-6234
Date of First Compliant Deposit:	30 April 2018
Date of Acceptance:	5 April 2018
Last Modified:	06 Nov 2023 16:58
URI:	https://orca.cardiff.ac.uk/id/eprint/111105

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