Distributed Graph Coloring Made Easy

Research output: Contribution to conferencePaperpeer-review


In this paper we present a deterministic CONGEST algorithm to compute an O(k)-vertex coloring in O(/k)+łog^∗n rounds, where Δis the maximum degree of the network graph and 1łeq kłeq O() 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 these and also simplifies the state of the art (+1)-coloring algorithm. At the cost of losing the full algorithm's simplicity we also provide a O(k)-coloring algorithm in O(s/k )+łog^∗n rounds. We also provide improved deterministic algorithms for ruling sets, and, additionally, we provide a tight characterization for one-round color reduction algorithms.

Original languageEnglish
Number of pages11
Publication statusPublished - 6 Jul 2021
Externally publishedYes
Event33rd ACM Symposium on Parallelism in Algorithms and Architectures: SPAA 2021 - Virtual, Online
Duration: 6 Jul 20218 Jul 2021


Conference33rd ACM Symposium on Parallelism in Algorithms and Architectures
CityVirtual, Online


  • Congest
  • Deterministic
  • Graph coloring
  • Local
  • Lower bound

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture


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