Abstract
We present a space-efficient algorithm for reporting all k intersections induced by a set of n line segments in the place. Our algorithm is an in-place variant of Balaban’s algorithm and runs in \(\mathcal{O}(n log^2_2 n + k)\) time using \(\mathcal{O}\)(1) extra words of memory over and above the space used for the input to the algorithm.
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References
Balaban, I.J.: An optimal algorithm for finding segments [sic!] intersections. In: Proceedings of the Eleventh Annual Symposium on Computational Geometry, pp. 211–219. ACM Press, New York (1995)
Bentley, J.L., Ottmann, T.A.: Algorithms for reporting and counting geometric intersections. IEEE Transactions on Computers C-28(9), 643–647 (1979)
Bose, P., Maheshwari, A., Morin, P., Morrison, J., Smid, M., Vahrenhold, J.: Space-efficient geometric divide-and-conquer algorithms. Computational Geometry: Theory & Applications, 2005. To appear, accepted November 2004. An extend abstract appeared in Proceedings of the 20th European Workshop on Computational Geometry, pp. 65–68 (2004)
Brönnimann, H., Chan, T.M.-Y., Chen, E.Y.: Towards in-place geometric algorithms. In: Proceedings of the Twentieth Annual Symposium on Computational Geometry, pp. 239–246. ACM Press, New York (2004)
Brönnimann, H., Iacono, J., Katajainen, J., Morin, P., Morrison, J., Toussaint, G.T.: Optimal in-place planar convex hull algorithms. Theoretical Computer Science 321(1), 25–40 (2004); An extended abstract appeared in the Proceedings of the Fifth Latin American Symposium on Theoretical Informatics, pp. 494–507 (2002)
Chazelle, B.M., Guibas, L.J.: Fractional cascading: I. A data structuring technique. Algorithmica 1(2), 133–162 (1986)
Chen, E.Y., Chan, T.M.-Y.: A space-efficient algorithm for line segment intersection. In: Proceedings of the 15th Canadian Conference on Computational Geometry, pp. 68–71 (2003)
Floyd, R.W.: Algorithm 245: Treesort. Communications of the ACM 7(12), 701 (1964)
Geffert, V., Katajainen, J., Pasanen, T.: Asymptotically efficient in-place merging. Theoretical Computer Science 237(1-2), 159–181 (2000)
Handbook of Discrete and Computational Geometry. In: Goodman, J.E., O’Rourke, J. (eds.) Discrete Mathematics and its Applications, 2nd edn., CRC Press, Boca Raton (2004)
Katajainen, J., Pasanen, T.: Stable minimum space partitioning in linear time. BIT 32, 580–585 (1992)
Mount, D.M.: Geometric intersection. In: Goodman and O’Rourke [10], ch. 38, pp. 857–876
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Vahrenhold, J. (2005). Line-Segment Intersection Made In-Place. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_14
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DOI: https://doi.org/10.1007/11534273_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28101-6
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