Book Embeddings and Point-Set Embeddings of Series-Parallel Digraphs

  • Emilio Di Giacomo
  • Walter Didimo
  • Giuseppe Liotta
  • Stephen K. Wismath
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2528)

Abstract

An optimal O(n)-time algorithm to compute an upward twopage book embedding of a series-parallel digraph with n vertices is presented. A previous algorithm of Alzohairi and Rival [1] runs in O(n 3) time and assumes that the input series-parallel digraph does not have transitive edges. One consequence of our result is that series-parallel (undirected) graphs are necessarily sub-hamiltonian. This extends a previous result by Chung, Leighton, and Rosenberg [5] who proved subhamiltonicity for a subset of planar series-parallel graphs. Also, this paper investigates the problem of mapping planar digraphs onto a given set of points in the plane, so that the edges are drawn upward planar. This problem is called the upward point-set embedding problem. The equivalence between the problem of computing an upward two-page book embedding and an upward point-set embedding with at most one bend per edge on any given set of points is proved. An O(n log n)-time algorithm for computing an upward point-set embedding with at most one bend per edge on any given set of points for planar series-parallel digraphs is presented.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  • Walter Didimo
    • 1
  • Giuseppe Liotta
    • 1
  • Stephen K. Wismath
    • 2
  1. 1.Dipartimento di Ingegneria Elettronica e dell’InformazioneUniversità degli Studi di PerugiaPerugiaItaly
  2. 2.Department of Mathematics and Computer ScienceUniversity of LethbridgeLethbridgeCanada

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