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Improved Distributed Algorithms for Coloring Interval Graphs with Application to Multicoloring Trees

  • Magnús M. Halldórsson
  • Christian KonradEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10641)

Abstract

We give a distributed \((1+\epsilon )\)-approximation algorithm for the minimum vertex coloring problem on interval graphs, which runs in the \(\mathcal {LOCAL}\) model and operates in \(\mathrm {O}(\frac{1}{\epsilon } \log ^* n)\) rounds. If nodes are aware of their interval representations, then the algorithm can be adapted to the \(\mathcal {CONGEST}\) model using the same number of rounds. Prior to this work, only constant factor approximations using \(\mathrm {O}(\log ^* n)\) rounds were known [12]. Linial’s ring coloring lower bound implies that the dependency on \(\log ^* n\) cannot be improved. We further prove that the dependency on \(\frac{1}{\epsilon }\) is also optimal.

To obtain our \(\mathcal {CONGEST}\) model algorithm, we develop a color rotation technique that may be of independent interest. We demonstrate that color rotations can also be applied to obtain a \((1+\epsilon )\)-approximate multicoloring of directed trees in \(\mathrm {O}( \frac{1}{\epsilon } \log ^* n)\) rounds.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.ICE-TCS, School of Computer ScienceReykjavik UniversityReykjavikIceland
  2. 2.Department of Computer Science, Centre for Discrete Mathematics and its Applications (DIMAP)University of WarwickCoventryUK

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