The support of integer optimal solutions

Aliev I, De Loera JA, Eisenbrand F, Oertel T, Weismantel R (2018)

Publication Type: Journal article

Publication year: 2018


Book Volume: 28

Pages Range: 2152-2157

Journal Issue: 3

DOI: 10.1137/17M1162792


The support of a vector is the number of nonzero components. We show that given anintegral m×n matrix A, the integer linear optimization problem maxfcT x: Ax = b; x = 0; x 2 Znghas an optimal solution whose support is bounded by 2m log(2pmkAk1), where kAk1 is the largestabsolute value of an entry of A. Compared to previous bounds, the one presented here is independentof the objective function. We furthermore provide a nearly matching asymptotic lower bound on thesupport of optimal solutions.

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Aliev, I., De Loera, J.A., Eisenbrand, F., Oertel, T., & Weismantel, R. (2018). The support of integer optimal solutions. SIAM Journal on Optimization, 28(3), 2152-2157.


Aliev, I., et al. "The support of integer optimal solutions." SIAM Journal on Optimization 28.3 (2018): 2152-2157.

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