On Interval Routing Schemes and treewidth

  • Hans L. Bodlaender
  • Richard B. Tann
  • Dimitris M. Thilikos
  • Jan van Leeuwen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1017)


In this paper, we investigate which processor networks allow k-label Interval Routing Schemes, under the assumption that costs of edges may vary. We show that for each fixed k≥1, the class of graphs allowing such routing schemes is closed under minor-taking in the domain of connected graphs, and hence has a linear time recognition algorithm. This result connects the theory of compact routing with the theory of graph minors and treewidth.

We also show that every graph that does not contain K2, r as a minor has treewidth at most 2r−2. In case the graph is planar, this bound can be lowered to r+2. As a consequence, graphs that allow k-label Interval Routing Schemes under dynamic cost edges have treewidth at most 4k, and treewidth at most 2k+3 if they are planar.

Similar results are shown for other types of Interval Routing Schemes.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  • Richard B. Tann
    • 1
    • 2
  • Dimitris M. Thilikos
    • 3
    • 4
  • Jan van Leeuwen
    • 1
  1. 1.Department of Computer ScienceUtrecht UniversityTB UtrechtThe Netherlands
  2. 2.Department of Computer ScienceUniversity of Sciences and Arts of OklahomaChickashaUSA
  3. 3.Computer Technology InstitutePatrasGreece
  4. 4.Department of Computer Engineering and InformaticsUniversity of PatrasRioGreece

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