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Steinhaus's geometric location problem for random samples in the plane

Published online by Cambridge University Press:  01 July 2016

Dorit Hochbaum  and
J. Michael Steele
Dorit Hochbaum*
Affiliation:
Carnegie-Mellon University
J. Michael Steele*
Affiliation:
Stanford University
*
∗Postal address: Graduate School of Industrial Administration, Carnegie–Mellon University, Pittsburgh, PA 15213, U.S.A.
∗∗Postal address: Department of Statistics, Stanford University, Stanford, CA 94305, U.S.A.
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Abstract

Let

where Xi, 1 ≦ i ≦ n, are i.i.d. and uniformly distributed in [0, 1]2. It is proved that Mn ∽ cn1–p/2 a.s. for 1 ≦ p <2. This result is motivated by recent developments in the theory of algorithms and the theory of subadditive processes as well as by a well-known problem of H. Steinhaus.

Keywords

LOCATION PROBLEMk-MEDIAN PROBLEMPROBABILISTIC ALGORITHMSUBADDITIVE PROCESSSUBADDITIVE EUCLIDEAN FUNCTIONAL
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 1 , March 1982 , pp. 56 - 67
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research supported in part by the Office of Naval Research Contract N00014-76-C-0475.

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