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 Scopus citations

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 publicationGraph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers
Pages183-194
Number of pages12
DOIs
StatePublished - Mar 9 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)0302-9743
ISSN (Electronic)1611-3349

Other

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Drawing trees with perfect angular resolution and polynomial area'. Together they form a unique fingerprint.

  • 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 Graph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers (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