Reducibility bounds of objective functions over the integers

Friedrich Eisenbrand, Christoph Hunkenschröder, Kim-Manuel Klein, Martin Koutecký, Asaf Levin, Shmuel Onn

Abstract: We study the settings where we are given a separable objective function of n variables defined in a given box of integers. We show that in many cases we can replace the given objective function by a new function with a much smaller domain. Our results apply to linear functions as well as to nonlinear separable convex objective functions.