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Near-optimal distributed edge coloring

  • Session 8. Chair: Michael Juenger
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Book cover Algorithms — ESA '95 (ESA 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 979))

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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+logs Δ loglog Δ).

Both results hold with probability arbitrarily close to 1 as long as Δ(G) =Ω(log1+d n), 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.

Work done partly while at the Max-Planck-Institute für Informatik supported by the ESPRIT Basic Research Actions Program of the EC under contract No. 7141 (project ALCOM II).

Supported by an Ercim postdoctoral fellowship.

Basic Research in Computer Science, Centre of the Danish National Research Foundation.

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Author information

Author notes

  1. Alessandro Panconesi

    Present address: Fachbereich Mathematik, MA 6-1, TU Berlin, Str. des 17 Juni 136, 10623, Berlin

Authors and Affiliations

  1. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, DK-8000, Aarhus C, Denmark

    Devdatt Dubhashi

  2. Centrum voor Wiskunde en Informatica 413 Kruislaan, 1098, SJ, Amsterdam, Holland

    Alessandro Panconesi

Authors
  1. Devdatt Dubhashi
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  2. Alessandro Panconesi
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Paul Spirakis

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© 1995 Springer-Verlag Berlin Heidelberg

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Dubhashi, D., Panconesi, A. (1995). Near-optimal distributed edge coloring. In: Spirakis, P. (eds) Algorithms — ESA '95. ESA 1995. Lecture Notes in Computer Science, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60313-1_162

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  • DOI: https://doi.org/10.1007/3-540-60313-1_162

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60313-9

  • Online ISBN: 978-3-540-44913-3

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