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Open Access Publications from the University of California

The support of integer optimal solutions

  • Author(s): Aliev, I
  • De Loera, JA
  • Eisenbrand, F
  • Oertel, T
  • Weismantel, R
  • et al.

© 2018 Society for Industrial and Applied Mathematics. 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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