Upward straight-line embeddings of directed graphs into point sets

Carla Binucci, Emilio Di Giacomo, Walter Didimo, Alejandro Estrella-Balderrama, Fabrizio Frati, Stephen G Kobourov, Giuseppe Liotta

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In this paper we study the problem of computing an upward straight-line embedding of a planar DAG (directed acyclic graph) G into a point set S, i.e. a planar drawing of G such that each vertex is mapped to a point of S, each edge is drawn as a straight-line segment, and all the edges are oriented according to a common direction. In particular, we show that no biconnected DAG admits an upward straight-line embedding into every point set in convex position. We provide a characterization of the family of DAGs that admit an upward straight-line embedding into every convex point set such that the points with the largest and the smallest y-coordinate are consecutive in the convex hull of the point set. We characterize the family of DAGs that contain a Hamiltonian directed path and that admit an upward straight-line embedding into every point set in general position. We also prove that a DAG whose underlying graph is a tree does not always have an upward straight-line embedding into a point set in convex position and we describe how to construct such an embedding for a DAG whose underlying graph is a path. Finally, we give results about the embeddability of some sub-classes of DAGs whose underlying graphs are trees on point set in convex and in general position.

Original languageEnglish (US)
Pages (from-to)219-232
Number of pages14
JournalComputational Geometry: Theory and Applications
Volume43
Issue number2 SPEC. ISS.
DOIs
StatePublished - Feb 2010
Externally publishedYes

Fingerprint

Hamiltonians
Directed graphs
Straight Line
Point Sets
Directed Graph
Directed Acyclic Graph
Graph in graph theory
Embeddability
Path
Line segment
Convex Hull
Convex Sets
Consecutive
Computing
Vertex of a graph

Keywords

  • Graph drawing
  • Point-set embedding
  • Upward drawings

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mathematics
  • Control and Optimization
  • Geometry and Topology

Cite this

Binucci, C., Di Giacomo, E., Didimo, W., Estrella-Balderrama, A., Frati, F., Kobourov, S. G., & Liotta, G. (2010). Upward straight-line embeddings of directed graphs into point sets. Computational Geometry: Theory and Applications, 43(2 SPEC. ISS.), 219-232. https://doi.org/10.1016/j.comgeo.2009.07.002

Upward straight-line embeddings of directed graphs into point sets. / Binucci, Carla; Di Giacomo, Emilio; Didimo, Walter; Estrella-Balderrama, Alejandro; Frati, Fabrizio; Kobourov, Stephen G; Liotta, Giuseppe.

In: Computational Geometry: Theory and Applications, Vol. 43, No. 2 SPEC. ISS., 02.2010, p. 219-232.

Research output: Contribution to journalArticle

Binucci, C, Di Giacomo, E, Didimo, W, Estrella-Balderrama, A, Frati, F, Kobourov, SG & Liotta, G 2010, 'Upward straight-line embeddings of directed graphs into point sets', Computational Geometry: Theory and Applications, vol. 43, no. 2 SPEC. ISS., pp. 219-232. https://doi.org/10.1016/j.comgeo.2009.07.002
Binucci, Carla ; Di Giacomo, Emilio ; Didimo, Walter ; Estrella-Balderrama, Alejandro ; Frati, Fabrizio ; Kobourov, Stephen G ; Liotta, Giuseppe. / Upward straight-line embeddings of directed graphs into point sets. In: Computational Geometry: Theory and Applications. 2010 ; Vol. 43, No. 2 SPEC. ISS. pp. 219-232.
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