LIPIcs.SoCG.2017.17.pdf
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Reachability in a Planar Subdivision with Direction Constraints
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33rd International Symposium on Computational Geometry (SoCG 2017)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Computational Geometry (SoCG) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2017-06-20
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Daniel Binham, Pedro Machado Manhaes de Castro, and Antoine Vigneron. Reachability in a Planar Subdivision with Direction Constraints. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.SoCG.2017.17
https://doi.org/10.4230/LIPIcs.SoCG.2017.17
Abstract
Given a planar subdivision with n vertices, each face having a cone of possible directions of travel, our goal is to decide which vertices of the subdivision can be reached from a given starting point s. We give an O(n log n)-time algorithm for this problem, as well as an Omega(n log n) lower bound in the algebraic computation tree model. We prove that the generalization where two cones of directions per face are allowed is NP-hard.
Keywords
- Design and analysis of geometric algorithms
- Path planning
- Reachability
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References
- Michael Ben-Or. Lower bounds for algebraic computation trees. In Proc. 15th ACM Symposium on Theory of Computing, pages 80-86, 1983. URL: http://dx.doi.org/10.1145/800061.808735.
-
Siu-Wing Cheng and Jiongxin Jin. Approximate shortest descending paths. In Proc. 24th ACM-SIAM Symposium on Discrete Algorithms, pages 144-155, 2013.
-
Siu-Wing Cheng, Hyeon-Suk Na, Antoine Vigneron, and Yajun Wang. Approximate shortest paths in anisotropic regions. SIAM Journal on Computing, 38(3):802-824, 2008.
-
Mark de Berg, Herman J. Haverkort, and Constantinos P. Tsirogiannis. Implicit flow routing on terrains with applications to surface networks and drainage structures. In Proc. 22nd ACM-SIAM Symposium on Discrete Algorithms, pages 285-296, 2011.
- Mark de Berg and Marc J. van Kreveld. Trekking in the alps without freezing or getting tired. Algorithmica, 18(3):306-323, 1997. URL: http://dx.doi.org/10.1007/PL00009159.
- John H. Reif and Zheng Sun. Movement planning in the presence of flows. Algorithmica, 39(2):127-153, 2004. URL: http://dx.doi.org/10.1007/s00453-003-1079-5.
- Zheng Sun and John H. Reif. On finding energy-minimizing paths on terrains. IEEE Transactions on Robotics, 21(1):102-114, 2005. URL: http://dx.doi.org/10.1109/TRO.2004.837232.
-
Robert Endre Tarjan. Data Structures and Network Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1983.