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”.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-540-73951-7_26
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