DOI: 10.1145/3605896 ISSN:

Distributed Graph Coloring Made Easy

Yannic Maus
  • Computational Theory and Mathematics
  • Computer Science Applications
  • Hardware and Architecture
  • Modeling and Simulation
  • Software

In this paper, we present a deterministic \(\mathsf {CONGEST} \) algorithm to compute an O ( )-vertex coloring in O ( Δ / k ) + log  * n rounds, where Δ is the maximum degree of the network graph and k ≥ 1 can be freely chosen. The algorithm is extremely simple: Each node locally computes a sequence of colors and then it tries colors from the sequence in batches of size k . Our algorithm subsumes many important results in the history of distributed graph coloring as special cases, including Linial’s color reduction [Linial, FOCS’87], the celebrated locally iterative algorithm from [Barenboim, Elkin, Goldenberg, PODC’18], and various algorithms to compute defective and arbdefective colorings. Our algorithm can smoothly scale between several of these previous results and also simplifies the state of the art ( Δ + 1)-coloring algorithm. At the cost of losing some of the algorithm’s simplicity we also provide a O ( )-coloring algorithm in \(O(\sqrt {\Delta /k})+\log ^{*} n \) rounds. We also provide improved deterministic algorithms for ruling sets, and, additionally, we provide a tight characterization for 1-round color reduction algorithms.

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