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 language | English |
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Pages (from-to) | 143-156 |
Number of pages | 14 |
Journal | Computational Geometry: Theory and Applications |
Volume | 11 |
Issue number | 3-4 |
DOIs | |
State | Published - 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