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Diameter Determination on Restricted Graph Families

  • Derek G. Corneil
  • Feodor F. Dragan
  • Michel Habib
  • Christophe Paul
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)

Abstract

Determining the diameter of a graph is a fundamental graph operation, yet no efficient (i.e. quadratic time) algorithm is known. In this paper, we examine the diameter problem on chordal and AT-free graphs and show that a very simple (linear time) 2-sweep Lex-BFS algorithm identifies a vertex of maximum eccentricity unless the given graph has a specified induced subgraph (it was previously known that a single Lex-BFS algorithm is guaranteed to end at a vertex that is within 1 of the diameter for chordal and AT-free graphs). As a consequence of the forbidden induced subgraph result on chordal graphs, our algorithm is guaranteed to work optimally for directed path graphs (it was previously known that a single LexBFS algorithm is guaranteed to work optimally for interval graphs).

Keywords

Intersection Graph Switching Point Interval Graph Chordal Graph 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-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Derek G. Corneil
    • 1
  • Feodor F. Dragan
    • 2
  • Michel Habib
    • 3
  • Christophe Paul
    • 3
  1. 1.Dpt. of Computer ScienceUniversity of TorontoTorontoCanada
  2. 2.Dpt. of Computer ScienceUniversity of RostockRostockGermany
  3. 3.LIRMMUMR CNRS-Université de Montpellier IIMontpellier Cedex 5France

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