@inproceedings{c1157600462641c8bb20492fc6e51a9f,

title = "Geometric applications of posets",

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≥ 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.",

author = "Michael Segal and Klara Kedem",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1997.; 5th International Workshop on Algorithms and Data Structures, WADS 1997 ; Conference date: 06-08-1997 Through 08-08-1997",

year = "1997",

month = jan,

day = "1",

doi = "10.1007/3-540-63307-3_78",

language = "English",

isbn = "3540633073",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "402--415",

editor = "Frank Dehne and Jorg-Rudiger Sack and Andrew Rau-Chaplin and Roberto Tamassia",

booktitle = "Algorithms and Data Structures - 5th International Workshop, WADS 1997, Proceedings",

address = "Germany",

}