Point Location Algorithms of Minimum Size

M. Ziegler, V. Damerow, L. Finschi, in: Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG’02), 2002.

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Consider the classical point location problem: for a fixed arrangement of m hyperplanes and its induced partition of d-space report, upon input of some point, which face it lies in. With sufficient memory, this is easy to solve in logarithmic time O(log m). But how fast can algorithms (formalized as Linear Decision Trees) of *minimum* size be? The present work gives lower and upper bounds for the time complexity of point location under this constraint. They show that, in addition to m, the maximum number w of walls of a cell turns out to be a crucial parameter. We also consider a relaxation of the strict minimum-size condition allowing for constant factor overhead.
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Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG'02)
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Ziegler M, Damerow V, Finschi L. Point Location Algorithms of Minimum Size. In: Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG’02). ; 2002.
Ziegler, M., Damerow, V., & Finschi, L. (2002). Point Location Algorithms of Minimum Size. In Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG’02).
@inproceedings{Ziegler_Damerow_Finschi_2002, title={Point Location Algorithms of Minimum Size}, booktitle={Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG’02)}, author={Ziegler, Martin and Damerow, Valentina and Finschi, Lukas}, year={2002} }
Ziegler, Martin, Valentina Damerow, and Lukas Finschi. “Point Location Algorithms of Minimum Size.” In Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG’02), 2002.
M. Ziegler, V. Damerow, and L. Finschi, “Point Location Algorithms of Minimum Size,” in Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG’02), 2002.
Ziegler, Martin, et al. “Point Location Algorithms of Minimum Size.” Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG’02), 2002.

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