DeepAI

We present an O(log^3log n)-round distributed algorithm for the (Δ+1)-coloring problem, where each node broadcasts only one O(log n)-bit message per round to its neighbors. Previously, the best such broadcast-based algorithm required O(log n) rounds. If Δ∈Ω(log^3 n), our algorithm runs in O(log^* n) rounds. Our algorithm's round complexity matches state-of-the-art in the much more powerful CONGEST model [Halldórsson et al., STOC'21 PODC'22], where each node sends one different message to each of its neighbors, thus sending up to Θ(nlog n) bits per round. This is the best complexity known, even if message sizes are unbounded. Our algorithm is simple enough to be implemented in even weaker models: we can achieve the same O(log^3log n) round complexity if each node reads its received messages in a streaming fashion, using only O(log^3 n)-bit memory. Therefore, we hope that our algorithm opens the road for adopting the recent exciting progress on sublogarithmic-time distributed (Δ+1)-coloring algorithms in a wider range of (theoretical or practical) settings.

08/10/2020

### Coloring Fast Without Learning Your Neighbors' Colors

We give an improved randomized CONGEST algorithm for distance-2 coloring...
12/28/2020

### Efficient Randomized Distributed Coloring in CONGEST

Distributed vertex coloring is one of the classic problems and probably ...
01/16/2023

### A Distributed Palette Sparsification Theorem

Is fully decentralized graph streaming possible? We consider this questi...
12/06/2022

### Non-trivial lower bound for 3-coloring the ring in the quantum LOCAL model

We consider the LOCAL model of distributed computing, where in a single ...
09/18/2019

### Message Reduction in the Local Model is a Free Lunch

A new spanner construction algorithm is presented, working under the LOC...
06/12/2019

### Collaborative Broadcast in O(log log n) Rounds

We consider the multihop broadcasting problem for n nodes placed uniform...
10/30/2020

### Dynamic Distributed MIS with Improved Bounds

The problem of maintaining a maximal independent set (MIS) in a dynamic ...
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