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.
Work partially supported by ESF EuroGIGA GraDR, by the MIUR project AMANDA “Algorithmics for MAssive and Networked DAta”, prot. 2012C4E3KT_001, and by the EU FP7 STREP Project ”Leone: From Global Measurements to Local Management”, no. 317647.
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References
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)
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)
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)
Dumitrescu, A., Mitchell, J.S.B.: Approximation algorithms for TSP with neighborhoods in the plane. J. Algorithms 48(1), 135–159 (2003)
Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)
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)
Löffler, M., van Kreveld, M.J.: Largest and smallest convex hulls for imprecise points. Algorithmica 56(2), 235–269 (2010)
Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput. 11, 185–225 (1982)
Lyons, K.A., Meijer, H., Rappaport, D.: Algorithms for cluster busting in anchored graph drawing. J. Graph Algorithms Appl. 2(1) (1998)
Patrignani, M.: On extending a partial straight-line drawing. International Journal of Foundations of Computer Science (IJFCS) 17(5), 1061–1069 (2006)
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Angelini, P. et al. (2014). Anchored Drawings of Planar Graphs. In: Duncan, C., Symvonis, A. (eds) Graph Drawing. GD 2014. Lecture Notes in Computer Science, vol 8871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45803-7_34
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DOI: https://doi.org/10.1007/978-3-662-45803-7_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-45802-0
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