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

15 Scopus citations

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

Keywords

  • Graph drawing
  • Point-set embedding
  • Upward drawings

ASJC Scopus subject areas

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

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  • 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