# Improving the Cook et al. Proximity Bound Given Integral Valued Constraints

@inproceedings{Celaya2022ImprovingTC, title={Improving the Cook et al. Proximity Bound Given Integral Valued Constraints}, author={Marcel Celaya and Stefan Kuhlmann and Joseph Paat and Robert Weismantel}, booktitle={IPCO}, year={2022} }

Consider a linear program of the form max cx : Ax ≤ b, where A is an m × n integral matrix. In 1986 Cook, Gerards, Schrijver, and Tardos proved that, given an optimal solution x, if an optimal integral solution z exists, then it may be chosen such that ‖x − z‖ ∞ < n∆, where ∆ is the largest magnitude of any subdeterminant of A. Since then an open question has been to improve this bound, assuming that b is integral valued too. In this manuscript we show that n∆ can be replaced with n/2…

## One Citation

A Colorful Steinitz Lemma with Applications to Block Integer Programs

- Mathematics
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The Steinitz constant in dimension d is the smallest value c(d) such that for any norm on R and for any finite zero-sum sequence in the unit ball, the sequence can be permuted such that the norm of…

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