Distributed Santa Claus via Global Rounding

TL;DR

This paper explores the distributed Santa Claus problem in the CONGEST model, providing the first approximation algorithms and establishing tight bounds on their round complexity.

Contribution

It introduces the first distributed algorithms for the Santa Claus problem and proves tight bounds on their round complexity in the CONGEST model.

Findings

Approximation complexity is Θ(√n + D) rounds.

Lower bound of Ω(√n + D) rounds applies to any approximation.

First results for distributed Santa Claus problem in the CONGEST model.

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.