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The support of integer optimal solutions

Aliev, I., De Loera, J. A., Eisenbrand, F., Oertel, T. 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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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: 25 Nov 2020 03:11

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