Point-Set Embedding of Trees with Edge Constraints

(Extended Abstract)
  • Emilio Di Giacomo
  • Walter Didimo
  • Giuseppe Liotta
  • Henk Meijer
  • Stephen Wismath
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)


Given a graph G with n vertices and a set S of n points in the plane, a point-set embedding of G on S is a planar drawing such that each vertex of G is mapped to a distinct point of S. A geometric point-set embedding is a point-set embedding with no edge bends. This paper studies the following problem: The input is a set S of n points, a planar graph G with n vertices, and a geometric point-set embedding of a subgraph G′ ⊂ G on a subset of S. The desired output is a point-set embedding of G on S that includes the given partial drawing of G′. We concentrate on trees and show how to compute the output in O(n2 logn) time and with at most 1 + 2 ⌈k/2 ⌉ bends per edge, where k is the number of vertices of the given subdrawing. We also prove that there are instances of the problem which require at least k − 3 bends for some of the edges.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  • Walter Didimo
    • 1
  • Giuseppe Liotta
    • 1
  • Henk Meijer
    • 2
  • Stephen Wismath
    • 3
  1. 1.Dip. di Ingegneria Elettronica e dell’InformazioneUniversità degli Studi di Perugia 
  2. 2.Roosevelt AcademyThe Netherlands
  3. 3.Department of Mathematics and Computer ScienceUniversity of Lethbridge 

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