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Near-optimal distributed edge coloring

  • Devdatt Dubhashi
  • Alessandro Panconesi
Session 8. Chair: Michael Juenger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 979)

Abstract

We give a distributed randomized algorithm to edge color a network. Given a graph G with n nodes and maximum degree Δ, the algorithm,
  • For any fixed λ>0, colours G with (1+λ)Δ colours in time O(log n).

  • For any fixed positive integer s, colours G with Δ+Δ/(log Δ)s=(1+o(1))Δ colours in time O(log n+logsΔ loglog Δ).

Both results hold with probability arbitrarily close to 1 as long as Δ(G) =Ω(log1+dn), for some d > 0. The algorithm is based on the Rödl Nibble, a probabilistic strategy introduced by Vojtech Rödl. The analysis involves a certain quasi-random phenomenon involving sets at the vertices of the graph.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Devdatt Dubhashi
    • 1
  • Alessandro Panconesi
    • 2
  1. 1.BRICS, Department of Computer ScienceUniversity of AarhusAarhus CDenmark
  2. 2.Centrum voor Wiskunde en Informatica 413 KruislaanSJ, AmsterdamHolland

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