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Starting with Nondeterminism: The Systematic Derivation of Linear-Time Graph Layout Algorithms

  • Hans L. Bodlaender
  • Michael R. Fellows
  • Dimitrios M. Thilikos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)

Abstract

This paper investigates algorithms for some related graph parameters. Each asks for a linear ordering of the vertices of the graph (or can be formulated as such), and there are constructive linear time algorithms for the fixed parameter versions of the problems. Examples are cutwidth, pathwidth, and directed or weighted variants of these. However, these algorithms have complicated technical details. This paper attempts to present these algorithms in a different more easily accessible manner, by showing that the algorithms can be obtained by a stepwise modification of a trivial hypothetical non-deterministic algorithm.

The methodology is applied for a generalisation of the cutwidth problem to weighted mixed graphs. As a consequence, we obtain new algorithmic results for various problems like modified cutwidth, and rederive known results for other related problems with simpler proofs.

Keywords

Algorithms and data structures graph algorithms algorithm design methodology graph layout problems finite state automata 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  • Michael R. Fellows
    • 2
  • Dimitrios M. Thilikos
    • 3
  1. 1.Institute of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.School of Electrical Engineering and Computer ScienceUniversity of NewcastleCallaghanAustralia
  3. 3.Departament de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain

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