Geometric applications of posets

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


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.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 5th International Workshop, WADS 1997, Proceedings
EditorsFrank Dehne, Jorg-Rudiger Sack, Andrew Rau-Chaplin, Roberto Tamassia
PublisherSpringer Verlag
Number of pages14
ISBN (Print)3540633073, 9783540633075
StatePublished - 1 Jan 1997
Event5th International Workshop on Algorithms and Data Structures, WADS 1997 - Halifax, Canada
Duration: 6 Aug 19978 Aug 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference5th International Workshop on Algorithms and Data Structures, WADS 1997

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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