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On Partitioning Interval and Circular-Arc Graphs into Proper Interval Subgraphs with Applications

  • Frédéric Gardi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)

Abstract

In this note, we establish that any interval or circular-arc graph with n vertices admits a partition into O(log n) proper interval subgraphs. This bound is shown to be asymptotically sharp for an infinite family of interval graphs. Moreover, the constructive proof yields a linear-time and space algorithm to compute such a partition. The second part of the paper is devoted to an application of this result, which has actually inspired this research: the design of an efficient approximation algorithm for a \(\mathcal{NP}\)-hard problem of planning working schedules.

Keywords

Linear Time Interval Graph Color Class Information Processing Letter Interval Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Frédéric Gardi
    • 1
  1. 1.Laboratoire d’Informatique FondamentaleParc Scientifique et Technologique de LuminyMarseille Cedex 9France

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