In this paper, we consider the Santa Claus problem in the CONGEST model. This NP-hard problem can be modeled as a bipartite graph of children and gifts where an edge indicates that a child desires a gift. Notably, each gift can have a different value. The goal is to assign the gifts to the children such that the least happy child is as happy as possible. Even though this is a well-studied problem in the sequential setting, we obtain the first results the distributed setting. In particular, we show that the complexity of computing an O(logn/loglogn)-approximation is Θ^(n+D) rounds, where our Ω(n+D)-round lower bound is even stronger and holds for any approximation.
@article{arxiv.2604.27983,
title = {Distributed Santa Claus via Global Rounding},
author = {Tijn de Vos and Leo Wennmann and Malte Baumecker and Yannic Maus and Florian Schager},
journal= {arXiv preprint arXiv:2604.27983},
year = {2026}
}