TY - GEN

T1 - Geometric applications of posets

AU - Segal, Michael

AU - Kedem, Klara

N1 - Funding Information:
* Corresponding author. 1 Work by Klara Kedem has been supported by a grant from the U.S.-Israeli Binational Science Foundation.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1997.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33745845685&partnerID=8YFLogxK

U2 - 10.1007/3-540-63307-3_78

DO - 10.1007/3-540-63307-3_78

M3 - Conference contribution

AN - SCOPUS:33745845685

SN - 3540633073

SN - 9783540633075

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 402

EP - 415

BT - Algorithms and Data Structures - 5th International Workshop, WADS 1997, Proceedings

A2 - Dehne, Frank

A2 - Sack, Jorg-Rudiger

A2 - Rau-Chaplin, Andrew

A2 - Tamassia, Roberto

PB - Springer Verlag

T2 - 5th International Workshop on Algorithms and Data Structures, WADS 1997

Y2 - 6 August 1997 through 8 August 1997

ER -