Geometric applications of posets

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 n-k-1 rectilinear farthest neighbors (or, equivalently, k 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/2 decide whether a query rectangle contains k points or less.

Original languageEnglish
Pages (from-to)143-156
Number of pages14
JournalComputational Geometry: Theory and Applications
Volume11
Issue number3-4
DOIs
StatePublished - 1 Jan 1998

Keywords

  • Algorithms
  • Distances
  • Nearest neighbors
  • Optimization
  • Posets

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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