TY - JOUR A1 - Deza, Antoine A1 - Pokutta, Sebastian A1 - Pournin, Lionel T1 - The complexity of geometric scaling JF - Operations Research Letters Y1 - 2024 U6 - https://doi.org/10.1016/j.orl.2023.11.010 VL - 52 SP - 107057 ER - TY - JOUR A1 - Deza, Antoine A1 - Onn, Shmuel A1 - Pokutta, Sebastian A1 - Pournin, Lionel T1 - Kissing polytopes JF - SIAM Journal on Discrete Mathematics N2 - We investigate the following question: How close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimization algorithms. We provide nearly matching bounds on this distance and discuss its exact computation. We also give similar bounds for disjoint rational polytopes whose binary encoding length is prescribed. Y1 - 2024 U6 - https://doi.org/10.1137/24M1640859 VL - 38 IS - 4 ER -