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Line-Distortion, Bandwidth and Path-Length of a Graph

  • Feodor F. Dragan
  • Ekkehard Köhler
  • Arne Leitert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)

Abstract

We investigate the minimum line-distortion and the minimum bandwidth problems on unweighted graphs and their relations with the minimum length of a Robertson-Seymour’s path-decomposition. The length of a path-decomposition of a graph is the largest diameter of a bag in the decomposition. The path-length of a graph is the minimum length over all its path-decompositions. In particular, we show: (i) if a graph G can be embedded into the line with distortion k, then G admits a Robertson-Seymour’s path-decomposition with bags of diameter at most k in G; (ii) for every class of graphs with path-length bounded by a constant, there exist an efficient constant-factor approximation algorithm for the minimum line-distortion problem and an efficient constant-factor approximation algorithm for the minimum bandwidth problem; (iii) there is an efficient 2-approximation algorithm for computing the path-length of an arbitrary graph; (iv) AT-free graphs and some intersection families of graphs have path-length at most 2; (v) for AT-free graphs, there exist a linear time 8-approximation algorithm for the minimum line-distortion problem and a linear time 4-approximation algorithm for the minimum bandwidth problem.

Keywords

Short Path Span Tree Chordal Graph Graph Class Arbitrary Graph 
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 International Publishing Switzerland 2014

Authors and Affiliations

  • Feodor F. Dragan
    • 1
  • Ekkehard Köhler
    • 2
  • Arne Leitert
    • 1
  1. 1.Department of Computer ScienceKent State UniversityKentUSA
  2. 2.Mathematisches InstitutBrandenburgische Technische Universität CottbusCottbusGermany

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