Abstract
Consider an n-vertex planar graph G. We present an O(n 4)-time algorithm for computing an embedding of G with minimum distance from the external face. This bound improves on the best previous bound by an O(n logn) factor. As a side effect, our algorithm improves the bounds of several algorithms that require the computation of a minimum depth embedding.
Work partially supported by EC - Fet Project DELIS - Contract no 001907 and by MUR under Project “MAINSTREAM: Algoritmi per strutture informative di grandi dimensioni e data streams”.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Angelini, P., Di Battista, G., Patrignani, M.: Computing a minimum-depth planar graph embedding in O(n 4) time. Tech. Rep. RT-DIA-116-2007, Dept. of Comp. Sci., Univ. Roma Tre (2007), http://web.dia.uniroma3.it/ricerca/rapporti/rapporti.php
Baker, B.S.: Approximation algorithms for NP-complete problems on planar graphs. J. of the Ass. for Comp. Mach. 41, 153–180 (1994)
Bienstock, D., Monma, C.L.: On the complexity of covering vertices by faces in a planar graph. SIAM-J. on Comp. 17, 53–76 (1988)
Bienstock, D., Monma, C.L.: On the complexity of embedding planar graphs to minimize certain distance measures. Algorithmica 5(1), 93–109 (1990)
Di Battista, G., Tamassia, R.: On-line planarity testing. SIAM J.C. 25(5), 956–997 (1996)
Di Giacomo, E., Didimo, W., Liotta, G., Meijer, H.: Computing radial drawings on the minimum number of circles. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 250–261. Springer, Heidelberg (2005)
Dolev, D., Leighton, F.T., Trickey, H.: Planar embedding of planar graphs. Adv. in Comp. Res. 2 (1984)
Pizzonia, M.: Minimum depth graph embeddings and quality of the drawings: An experimental analysis. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 397–408. Springer, Heidelberg (2006)
Pizzonia, M., Tamassia, R.: Minimum depth graph embedding. In: Paterson, M.S. (ed.) ESA 2000. LNCS, vol. 1879, pp. 356–357. Springer, Heidelberg (2000)
Robertson, N., Seymour, P.D.: Graph minors. III. Planar tree-width. J. Comb. Theory, Ser. B 36(1), 49–64 (1984)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Angelini, P., Di Battista, G., Patrignani, M. (2007). Computing a Minimum-Depth Planar Graph Embedding in O(n 4) Time . In: Dehne, F., Sack, JR., Zeh, N. (eds) Algorithms and Data Structures. WADS 2007. Lecture Notes in Computer Science, vol 4619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73951-7_26
Download citation
DOI: https://doi.org/10.1007/978-3-540-73951-7_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73948-7
Online ISBN: 978-3-540-73951-7
eBook Packages: Computer ScienceComputer Science (R0)