Drawing Trees with Perfect Angular Resolution and Polynomial Area

Christian A. Duncan, David Eppstein, Michael T. Goodrich, Stephen G Kobourov, Martin Nöllenburg

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We study methods for drawing trees with perfect angular resolution, i. e., with angles at each node v equal to 2π /d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.

Original languageEnglish (US)
Pages (from-to)157-182
Number of pages26
JournalDiscrete and Computational Geometry
Volume49
Issue number2
DOIs
StatePublished - 2013

Fingerprint

Line Drawing
Polynomials
Polynomial
Straight Line
Ordered Trees
Unordered
Arc of a curve
Drawing
Angle
Vertex of a graph
Style

Keywords

  • Circular-arc drawings
  • Lombardi drawings
  • Perfect angular resolution
  • Polynomial area
  • Straight-line drawings
  • Tree drawings

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology

Cite this

Drawing Trees with Perfect Angular Resolution and Polynomial Area. / Duncan, Christian A.; Eppstein, David; Goodrich, Michael T.; Kobourov, Stephen G; Nöllenburg, Martin.

In: Discrete and Computational Geometry, Vol. 49, No. 2, 2013, p. 157-182.

Research output: Contribution to journalArticle

Duncan, Christian A. ; Eppstein, David ; Goodrich, Michael T. ; Kobourov, Stephen G ; Nöllenburg, Martin. / Drawing Trees with Perfect Angular Resolution and Polynomial Area. In: Discrete and Computational Geometry. 2013 ; Vol. 49, No. 2. pp. 157-182.
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