Abstract
We show the power of posets in computational geometry by solving several problems posed on a set S of n points in the plane: (1) find the k rectilinear nearest neighbors to every point of S (extendable to higher dimensions), (2) enumerate the k largest (smallest) rectilinear distances in decreasing (increasing) order among the points of S, (3) given a distance δ > 0 report all the pairs of points that belong to S and are of rectilinear distance δ or more (less), covering \(k \geqslant \frac{n}{2}\)points of S by rectilinear (4) and circular (5) concentric rings, and (6) given a number \(k \geqslant \frac{n}{2}\)decide whether a query rectangle contains k points or less.
Work by Klara Kedem has been supported by a grant from the U.S.-Israeli Binational Science Foundation.
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© 1997 Springer-Verlag Berlin Heidelberg
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Segal, M., Kedem, K. (1997). Geometric Applications of Posets. In: Dehne, F., Rau-Chaplin, A., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1997. Lecture Notes in Computer Science, vol 1272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63307-3_78
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DOI: https://doi.org/10.1007/3-540-63307-3_78
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