Polynomial Lower Bound for Distributed Graph Coloring in a Weak LOCAL Model

  • Dan Hefetz
  • Fabian Kuhn
  • Yannic Maus
  • Angelika Steger
Conference paper

DOI: 10.1007/978-3-662-53426-7_8

Volume 9888 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Hefetz D., Kuhn F., Maus Y., Steger A. (2016) Polynomial Lower Bound for Distributed Graph Coloring in a Weak LOCAL Model. In: Gavoille C., Ilcinkas D. (eds) Distributed Computing. DISC 2016. Lecture Notes in Computer Science, vol 9888. Springer, Berlin, Heidelberg

Abstract

We show an \(\varOmega \big (\varDelta ^{\frac{1}{3}-\frac{\eta }{3}}\big )\) lower bound on the runtime of any deterministic distributed \(\mathcal {O}\big (\varDelta ^{1+\eta }\big )\)-graph coloring algorithm in a weak variant of the \(\mathsf {LOCAL}\) model.

In particular, given a network graph \(G=(V,E)\), in the weak \(\mathsf {LOCAL}\) model nodes communicate in synchronous rounds and they can use unbounded local computation. The nodes have no identifiers, but instead, the computation starts with an initial valid vertex coloring. A node can broadcast a single message of unbounded size to its neighbors and receives the set of messages sent to it by its neighbors.

The proof uses neighborhood graphs and improves their understanding in general such that it might help towards finding a lower (runtime) bound for distributed graph coloring in the standard \(\mathsf {LOCAL}\) model.

Keywords

Lower bound Distributed graph coloring Color reduction Neighborhood graphs LOCAL model Distributed symmetry breaking 

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Dan Hefetz
    • 1
    • 2
  • Fabian Kuhn
    • 3
  • Yannic Maus
    • 3
  • Angelika Steger
    • 4
  1. 1.Hebrew UniversityJerusalemIsrael
  2. 2.Tel Aviv UniversityTel AvivIsrael
  3. 3.University of FreiburgFreiburg im BreisgauGermany
  4. 4.ETH ZurichZürichSwitzerland