Anchored Drawings of Planar Graphs

  • Patrizio Angelini
  • Giordano Da Lozzo
  • Marco Di Bartolomeo
  • Giuseppe Di Battista
  • Seok-Hee Hong
  • Maurizio Patrignani
  • Vincenzo Roselli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)

Abstract

In this paper we study the Anchored Graph Drawing (AGD) problem: Given a planar graph G, an initial placement for its vertices, and a distance d, produce a planar straight-line drawing of G such that each vertex is at distance at most d from its original position.

We show that the AGD problem is NP-hard in several settings and provide a polynomial-time algorithm when d is the uniform distance L  ∞  and edges are required to be drawn as horizontal or vertical segments.

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References

  1. 1.
    Abellanas, M., Aiello, A., Hernández, G., Silveira, R.I.: Network drawing with geographical constraints on vertices. In: Actas XI Encuentros de Geom. Comput., pp. 111–118 (2005)Google Scholar
  2. 2.
    Angelini, P., Da Lozzo, G., Di Battista, G., Frati, F.: Strip planarity testing. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 37–48. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Cabello, S., Mohar, B.: Adding one edge to planar graphs makes crossing number and 1-planarity hard. SIAM J. Comput. 42(5), 1803–1829 (2013)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Dumitrescu, A., Mitchell, J.S.B.: Approximation algorithms for TSP with neighborhoods in the plane. J. Algorithms 48(1), 135–159 (2003)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Godau, M.: On the difficulty of embedding planar graphs with inaccuracies. In: Tamassia, R., Tollis, I.G. (eds.) GD 1994. LNCS, vol. 894, pp. 254–261. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  7. 7.
    Löffler, M., van Kreveld, M.J.: Largest and smallest convex hulls for imprecise points. Algorithmica 56(2), 235–269 (2010)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput. 11, 185–225 (1982)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Lyons, K.A., Meijer, H., Rappaport, D.: Algorithms for cluster busting in anchored graph drawing. J. Graph Algorithms Appl. 2(1) (1998)Google Scholar
  10. 10.
    Patrignani, M.: On extending a partial straight-line drawing. International Journal of Foundations of Computer Science (IJFCS) 17(5), 1061–1069 (2006)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Giordano Da Lozzo
    • 1
  • Marco Di Bartolomeo
    • 1
  • Giuseppe Di Battista
    • 1
  • Seok-Hee Hong
    • 2
  • Maurizio Patrignani
    • 1
  • Vincenzo Roselli
    • 1
  1. 1.Department of EngineeringRoma Tre UniversityItaly
  2. 2.School of Information TechnologiesThe University of SydneyAustralia

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