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≥ n/2 points of S by rectilinear (4) and circular (5) concentric rings, and (6) given a number k≥ n/2d ecide whether a query rectangle contains k points or less.
CITATION STYLE
Segal, M., & Kedem, K. (1997). Geometric applications of posets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1272, pp. 402–415). Springer Verlag. https://doi.org/10.1007/3-540-63307-3_78
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