Drawing trees with perfect angular resolution and polynomial area

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Citations (Scopus)

Abstract

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each vertex, 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)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages183-194
Number of pages12
Volume6502 LNCS
DOIs
StatePublished - 2011
Event18th International Symposium on Graph Drawing, GD 2010 - Konstanz, Germany
Duration: Sep 21 2010Sep 24 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6502 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other18th International Symposium on Graph Drawing, GD 2010
CountryGermany
CityKonstanz
Period9/21/109/24/10

Fingerprint

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

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Duncan, C. A., Eppstein, D., Goodrich, M. T., Kobourov, S. G., & Nöllenburg, M. (2011). Drawing trees with perfect angular resolution and polynomial area. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6502 LNCS, pp. 183-194). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6502 LNCS). https://doi.org/10.1007/978-3-642-18469-7_17

Drawing trees with perfect angular resolution and polynomial area. / Duncan, Christian A.; Eppstein, David; Goodrich, Michael T.; Kobourov, Stephen G; Nöllenburg, Martin.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6502 LNCS 2011. p. 183-194 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6502 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Duncan, CA, Eppstein, D, Goodrich, MT, Kobourov, SG & Nöllenburg, M 2011, Drawing trees with perfect angular resolution and polynomial area. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 6502 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6502 LNCS, pp. 183-194, 18th International Symposium on Graph Drawing, GD 2010, Konstanz, Germany, 9/21/10. https://doi.org/10.1007/978-3-642-18469-7_17
Duncan CA, Eppstein D, Goodrich MT, Kobourov SG, Nöllenburg M. Drawing trees with perfect angular resolution and polynomial area. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6502 LNCS. 2011. p. 183-194. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-18469-7_17
Duncan, Christian A. ; Eppstein, David ; Goodrich, Michael T. ; Kobourov, Stephen G ; Nöllenburg, Martin. / Drawing trees with perfect angular resolution and polynomial area. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6502 LNCS 2011. pp. 183-194 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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