Characterization of unlabeled level planar trees

Alejandro Estrella-Balderrama, J. Joseph Fowler, Stephen G Kobourov

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

7 Citations (Scopus)

Abstract

Consider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line ℓj = {(x, j) |x ∈ ℝ}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines ℓj forms a labeling of the vertices. Such a graph G with the labeling φ is called an n-level graph and is said to be n-level planar if it can be drawn with straight-line edges and no crossings while keeping each vertex on its own level. In this paper, we consider the class of trees that are n-level planar regardless of their labeling. We call such trees unlabeled level planar (ULP). Our contributions are three-fold. First, we provide a complete characterization of ULP trees in terms of a pair of forbidden subtrees. Second, we show how to draw ULP trees in linear time. Third, we provide a linear time recognition algorithm for ULP trees.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages367-379
Number of pages13
Volume4372 LNCS
StatePublished - 2007
Event14th International Symposium on Graph Drawing, GD 2006 - Karlsruhe, Germany
Duration: Sep 18 2006Sep 19 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4372 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other14th International Symposium on Graph Drawing, GD 2006
CountryGermany
CityKarlsruhe
Period9/18/069/19/06

Fingerprint

Labeling
Horizontal
Graph in graph theory
Distinct
Line
Recognition Algorithm
Threefolds
Linear-time Algorithm
Vertex of a graph
Bijection
Straight Line
Linear Time

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Estrella-Balderrama, A., Fowler, J. J., & Kobourov, S. G. (2007). Characterization of unlabeled level planar trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4372 LNCS, pp. 367-379). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4372 LNCS).

Characterization of unlabeled level planar trees. / Estrella-Balderrama, Alejandro; Fowler, J. Joseph; Kobourov, Stephen G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4372 LNCS 2007. p. 367-379 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4372 LNCS).

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

Estrella-Balderrama, A, Fowler, JJ & Kobourov, SG 2007, Characterization of unlabeled level planar trees. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4372 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4372 LNCS, pp. 367-379, 14th International Symposium on Graph Drawing, GD 2006, Karlsruhe, Germany, 9/18/06.
Estrella-Balderrama A, Fowler JJ, Kobourov SG. Characterization of unlabeled level planar trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4372 LNCS. 2007. p. 367-379. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Estrella-Balderrama, Alejandro ; Fowler, J. Joseph ; Kobourov, Stephen G. / Characterization of unlabeled level planar trees. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4372 LNCS 2007. pp. 367-379 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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