, Volume 45, Issue 4, pp 531–547 | Cite as

Book Embeddability of Series–Parallel Digraphs

  • Emilio Di Giacomo
  • Walter Didimo
  • Giuseppe Liotta
  • Stephen K. Wismath


In this paper we deal with the problem of computing upward two-page book embeddings of Two Terminal Series-Parallel (TTSP) digraphs, which are a subclass of series-parallel digraphs. An optimal O(n) time and space algorithm to compute an upward two-page book embedding of a TTSP-digraph with n vertices is presented. A previous algorithm of Alzohairi and Rival [1] runs in O(n3) time and assumes that the input series-parallel digraph does not have transitive edges. An application of this result to a computational geometry problem is also discussed. More precisely, upward two-page book embeddings are used to deal with the upward point-set embeddability problem, i.e., the problem of mapping planar digraphs onto a given set of points in the plane so that all edges are monotonically increasing in a common direction. The equivalence between upward two-page book embeddability and upward point-set embeddability 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 for TTSP-digraphs is presented.

Book embeddability Point set embedding 


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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Elettronica e dell'Informazione, Universita degli Studi di PerugiaPerugiaItaly
  2. 2.Department of Mathematics and Computer Science, University of LethbridgeLethbridge, Alberta, T1K 3M4Canada

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