Efficient randomized distributed coloring in CONGEST

Magnús M. Halldórsson, Fabian Kuhn, Yannic Maus, Tigran Tonoyan

Research output: Contribution to conferencePaperpeer-review


Distributed vertex coloring is one of the classic problems and probably also the most widely studied problems in the area of distributed graph algorithms. We present a new randomized distributed vertex coloring algorithm for the standard CONGEST model, where the network is modeled as an n-node graph G, and where the nodes of G operate in synchronous communication rounds in which they can exchange O(logn)-bit messages over all the edges of G. For graphs with maximum degree ?, we show that the (?+1)-list coloring problem (and therefore also the standard (?+1)-coloring problem) can be solved in O(log5logn) rounds. Previously such a result was only known for the significantly more powerful LOCAL model, where in each round, neighboring nodes can exchange messages of arbitrary size. The best previous (?+1)-coloring algorithm in the CONGEST model had a running time of O(log?+ log6logn) rounds. As a function of n alone, the best previous algorithm therefore had a round complexity of O(logn), which is a bound that can also be achieved by a na'ive folklore algorithm. For large maximum degree ?, our algorithm hence is an exponential improvement over the previous state of the art.

Original languageEnglish
Number of pages14
Publication statusPublished - 15 Jun 2021
Externally publishedYes
Event53rd Annual ACM SIGACT Symposium on Theory of Computing: STOC 2021 - Virtual, Online
Duration: 21 Jun 202125 Jun 2021


Conference53rd Annual ACM SIGACT Symposium on Theory of Computing
CityVirtual, Online


  • CONGEST model
  • deterministic vertex coloring
  • massively parallel computation

ASJC Scopus subject areas

  • Software


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