Sub-coloring and Hypo-coloring Interval Graphs

  • Rajiv Gandhi
  • Bradford GreeningJr.
  • Sriram Pemmaraju
  • Rajiv Raman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5911)

Abstract

In this paper, we study the sub-coloring and hypo-coloring problems on interval graphs. These problems have applications in job scheduling and distributed computing and can be used as “subroutines” for other combinatorial optimization problems. In the sub-coloring problem, given a graph G, we want to partition the vertices of G into minimum number of sub-color classes, where each sub-color class induces a union of disjoint cliques in G. In the hypo-coloring problem, given a graph G, and integral weights on vertices, we want to find a partition of the vertices of G into sub-color classes such that the sum of the weights of the heaviest cliques in each sub-color class is minimized. We present a “forbidden subgraph” characterization of graphs with sub-chromatic number k and use this to derive a 3-approximation algorithm for sub-coloring interval graphs. For the hypo-coloring problem on interval graphs, we first show that it is NP-complete, and then via reduction to the max-coloring problem, show how to obtain an O(logn)-approximation algorithm for it.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Rajiv Gandhi
    • 1
  • Bradford GreeningJr.
    • 1
  • Sriram Pemmaraju
    • 2
  • Rajiv Raman
    • 3
  1. 1.Department of Computer ScienceRutgers University-CamdenCamden
  2. 2.Department of Computer ScienceUniversity of IowaIowa City, Iowa
  3. 3.Max-Planck Institute for InformatikSaarbrückenGermany

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