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- Title
Order Distance in Regular Point Patterns.
- Authors
Miyagawa, Masashi
- Abstract
This article examines the kth nearest neighbor distance for three regular point patterns: square, triangular, and hexagonal lattices. The probability density functions of the kth nearest distance and the average kth nearest distances are theoretically derived for k=1, 2, ..., 7. As an application of the kth nearest distance, we consider a facility location problem with closing of facilities. The problem is to find the optimal regular pattern that minimizes the average distance to the nearest open facility. Assuming that facilities are closed independently and at random, we show that the triangular lattice is optimal if at least 68% of facilities are open by comparing the upper and lower bounds of the average distances.
- Subjects
LATTICE theory; PROBABILITY theory; DENSITY; DISTANCES; ARITHMETIC mean
- Publication
Geographical Analysis, 2009, Vol 41, Issue 1, p102
- ISSN
0016-7363
- Publication type
Article
- DOI
10.1111/j.1538-4632.2009.00737.x