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arXiv · 2604.27983

Distributed Santa Claus via Global Rounding

Tijn de Vos·Leo Wennmann·Malte Baumecker·Yannic Maus·Florian Schager
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Abstract

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 $\mathcal{O}(\log n/\log \log n)$-approximation is $\hat \Theta(\sqrt n+D)$ rounds, where our $\widetilde\Omega(\sqrt n+D)$-round lower bound is even stronger and holds for any approximation.

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Tijn de Vos, Leo Wennmann, Malte Baumecker, Yannic Maus, Florian Schager. 2026-04-30. Distributed Santa Claus via Global Rounding. https://arxiv.org/abs/2604.27983

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