A Fixed-Parameter Approach to Two-Layer Planarization

  • V. Dujmović
  • M. Fellows
  • M. Hallett
  • M. Kitching
  • Giuseppe Liotta
  • C. McCartin
  • N. Nishimura
  • P. Ragde
  • F. Rosamond
  • M. Suderman
  • S. Whitesides
  • David R. Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2265)

Abstract

A bipartite graph is biplanar if the vertices can be placed on two parallel lines (layers) in the plane such that there are no edge crossings when edges are drawn straight. The 2-Layer Planarization problem asks if k edges can be deleted from a given graph G so that the remaining graph is biplanar. This problem is NP-complete, as is the 1- Layer Planarization problem in which the permutation of the vertices in one layer is fixed. We give the following fixed parameter tractability results: an O(k ·6k+|G|) algorithm for 2-Layer Planarization and an O(3k· |G|) algorithm for 1-Layer Planarization, thus achieving linear time for fixed k.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • V. Dujmović
    • 1
  • M. Fellows
    • 4
  • M. Hallett
    • 1
  • M. Kitching
    • 1
  • Giuseppe Liotta
    • 2
  • C. McCartin
    • 5
  • N. Nishimura
    • 3
  • P. Ragde
    • 3
  • F. Rosamond
    • 4
  • M. Suderman
    • 1
  • S. Whitesides
    • 1
  • David R. Wood
    • 6
  1. 1.McGill UniversityCanada
  2. 2.Università di PerugiaItaly
  3. 3.University of WaterlooCanada
  4. 4.University of VictoriaCanada
  5. 5.Victoria University of WellingtonNew Zealand
  6. 6.University of SydneyAustralia

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