Distributed Coloring in the SLEEPING Model
Fabien Dufoulon, Pierre Fraigniaud, Mikaël Rabie, Hening Zheng
TL;DR
The paper studies energy-efficient distributed coloring in the SLEEPING model, showing that $(\Delta+1)$-coloring is achievable with polylogarithmic round complexity while keeping node awake time extremely small on average. It introduces a three-phase randomized-deterministic strategy for $(\deg+1)$-list-coloring: a fast initial randomized phase, a degree-reduction phase using a near-optimal subroutine, and a final deterministic coloring on the reduced graph. The main contributions are $O(1)$ expected average awake complexity, $O(\log\log n)$ worst-case awake complexity, and $O(\mathrm{poly}\log n)$ rounds, demonstrating substantial energy savings in the SLEEPING LOCAL model. This work advances the understanding of awake vs. round-time trade-offs in distributed graph coloring and raises questions about possible sub-$\log\log n$ awake complexities for fundamental local problems.
Abstract
In distributed network computing, a variant of the LOCAL model has been recently introduced, referred to as the SLEEPING model. In this model, nodes have the ability to decide on which round they are awake, and on which round they are sleeping. Two (adjacent) nodes can exchange messages in a round only if both of them are awake in that round. The SLEEPING model captures the ability of nodes to save energy when they are sleeping. In this framework, a major question is the following: is it possible to design algorithms that are energy efficient, i.e., where each node is awake for a few number of rounds only, without losing too much on the time efficiency, i.e., on the total number of rounds? This paper answers positively to this question, for one of the most fundamental problems in distributed network computing, namely $(Δ+1)$-coloring networks of maximum degree $Δ$. We provide a randomized algorithm with average awake-complexity constant, maximum awake-complexity $O(\log\log n)$ in $n$-node networks, and round-complexity $poly\!\log n$.