Asymptotics for geometric location problems over random samples
1999 ◽
Vol 31
(3)
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pp. 632-642
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Keyword(s):
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.
1973 ◽
Vol 16
(3)
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pp. 337-342
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2005 ◽
Vol 08
(04)
◽
pp. 669-680
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1980 ◽
Vol 87
(1)
◽
pp. 179-187
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1971 ◽
Vol 12
(4)
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pp. 433-440
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Keyword(s):
2014 ◽
Vol 58
(1)
◽
pp. 125-147
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1992 ◽
Vol 06
(03n04)
◽
pp. 281-320
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1955 ◽
Vol 51
(4)
◽
pp. 629-638
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2011 ◽
Vol 151
(3)
◽
pp. 521-539
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