1 results
Asymptotics for geometric location problems over random samples
- Part of
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- Journal:
- Advances in Applied Probability / Volume 31 / Issue 3 / September 1999
- Published online by Cambridge University Press:
- 01 July 2016, pp. 632-642
- Print publication:
- September 1999
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- Article
- Export citation
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Consider the basic location problem in which k locations from among n given points X1,…,Xn are to be chosen so as to minimize the sum M(k; X1,…,Xn) of the distances of each point to the nearest location. It is assumed that no location can serve more than a fixed finite number D of points. When the Xi, i ≥ 1, are i.i.d. random variables with values in [0,1]d and when k = ⌈n/(D+1)⌉ we show that
where α := α(D,d) is a positive constant, f is the density of the absolutely continuous part of the law of X1, and c.c. denotes complete convergence.
