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Faster output-sensitive skyline computation algorithm. (English) Zbl 1371.68294
Summary: We present the second output-sensitive skyline computation algorithm which is faster than the only existing output-sensitive skyline computation algorithm [D. G. Kirkpatrick and R. Seidel, “Output-size sensitive algorithms for finding maximal vectors”, in: Proceedings of the 1st annual symposium on computational geometry, SCG’85. New York, NY: Association for Computing Machinery (ACM). 89–96 (1985; doi:10.1145/323233.323246)] in worst case because our algorithm does not rely on the existence of a linear time procedure for finding medians.
##### MSC:
 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) 68Q25 Analysis of algorithms and problem complexity
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##### References:
 [1] Kirkpatrick, D. G.; Seidel, R., Output-size sensitive algorithms for finding maximal vectors, (Symposium on Computational Geometry, (1985)), 89-96 [2] Bentley, J. L., Multidimensional divide-and-conquer, Commun. ACM, 23, 4, 214-229, (1980) · Zbl 0434.68049 [3] Bentley, J. L.; Clarkson, K. L.; Levine, D. B., Fast linear expected-time algorithms for computing maxima and convex hulls, (SODA, (1990)), 179-187 · Zbl 0800.68959 [4] Bentley, J. L.; Kung, H. T.; Schkolnick, M.; Thompson, C. D., On the average number of maxima in a set of vectors and applications, J. ACM, 25, 4, 536-543, (1978) · Zbl 0388.68056 [5] Kung, H. T.; Luccio, F.; Preparata, F. P., On finding the maxima of a set of vectors, J. ACM, 22, 4, 469-476, (1975) · Zbl 0316.68030 [6] Hu, X.; Sheng, C.; Tao, Y.; Yang, Y.; Zhou, S., Output-sensitive skyline algorithms in external memory, (SODA, (2013)), 887-900 · Zbl 1423.68545 [7] Blum, M.; Floyd, R. W.; Pratt, V. R.; Rivest, R. L.; Tarjan, R. E., Time bounds for selection, J. Comput. Syst. Sci., 7, 4, 448-461, (1973) · Zbl 0278.68033 [8] Chan, T. M.; Lee, P., On constant factors in comparison-based geometric algorithms and data structures, (Symposium on Computational Geometry, (2014)), 40 · Zbl 1395.68295 [9] Luccio, F.; Preparata, F., On finding the maxima of a set of vectors, (1973), Instituto di Scienze dell’Informazione, Università di Pisa, 56100 Corso Italia 40 [10] Chan, T. M., Optimal output-sensitive convex hull algorithms in two and three dimensions, Discrete Comput. Geom., 16, 4, 361-368, (1996) · Zbl 0857.68111
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