Asymptotics of power-weighted Euclidean functionals
Let {Xi: i[greater-or-equal, slanted]1} be i.i.d. points in , d[greater-or-equal, slanted]2, and let LMM({X1,...,Xn},p), LMST({X1,...,Xn},p), LTSP({X1,...,Xn},p), be the length of the minimal matching, the minimal spanning tree, the traveling salesman problem, respectively, on {X1,...,Xn} with weight function w(e)=ep. If the common distribution satisfies certain regularity conditions, then the strong law of large numbers for the above three Euclidean functionals, 1[less-than-or-equals, slant]p<d, has been obtained. In this paper we show that the same type of result holds for 0<p<1.
Year of publication: |
1999
|
---|---|
Authors: | Lee, Sungchul |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 79.1999, 1, p. 109-116
|
Publisher: |
Elsevier |
Keywords: | Minimal matching Minimal spanning tree Traveling salesman problem |
Saved in:
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