Ultrafast Distributed Coloring of High Degree Graphs

2021/05/10 by Halldórsson, Magnús M., Nolin, Alexandre, Tonoyan, Tigran
#Data Structures and Algorithms (cs.DS) #Distributed #FOS: Computer and information sciences #Parallel #and Cluster Computing (cs.DC)

paper · doi:10.48550/arxiv.2105.04700

Abstract

We give a new randomized distributed algorithm for the Δ+1-list coloring problem. The algorithm and its analysis dramatically simplify the previous best result known of Chang, Li, and Pettie [SICOMP 2020]. This allows for numerous refinements, and in particular, we can color all n-node graphs of maximum degree Δ≥ log^2+Ω(1) n in O(log^* n) rounds. The algorithm works in the CONGEST model, i.e., it uses only O(log n) bits per message for communication. On low-degree graphs, the algorithm shatters the graph into components of size poly(log n) in O(log^* Δ) rounds, showing that the randomized complexity of Δ+1-list coloring in CONGEST depends inherently on the deterministic complexity of related coloring problems.

Related

• Efficient Randomized Distributed Coloring in CONGEST
• Fast Distributed Brooks' Theorem
• Near-Optimal Distributed Degree+1 Coloring
• Faster Distributed Δ-Coloring via Ruling Subgraphs
• Faster Deterministic Distributed Coloring Through Recursive List Coloring