Marcel Celaya (TU)
01.08.2019 – 31.12.2020
A classic result of Cook et al. (1986) bounds the distances between optimal solutions of integer linear programs and optimal solutions of the corresponding linear relaxations. Their bound is the product of the dimension and a parameter Δ, which quantifies sub-determinants of the underlying linear inequalities. We intend to study this bound both, deterministically and probabilistically. In particular, in the deterministic setting we want to make the bound independent of the dimension. This would be a first step to show that Δ is a fundamental parameter to make high dimensional integer linear optimization problems tractable.
W. Cook, A.M.H. Gerards, A. Schrijver, and E. Tardos. Sensitivity theorems in integer linear programming. Math. Programming, 34(3):251–264, 1986.
F. Eisenbrand and R. Weismantel. Proximity results and faster algorithms for integer pro- gramming using the Steinitz lemma. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 808–816. SIAM, Philadelphia, PA, 2018.
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