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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)

Abstract

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(n 2 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.

Keywords

Planar Graph Convex Polygon Dual Graph Outerplanar Graph Planar Drawing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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