Worst case asymptotics of power-weighted Euclidean functionals

Authors:
Sungchul Lee
Affiliations:
Department of Mathematics, Yonsei University, Seoul 120-749, South Korea
Venue:
Discrete Mathematics
Year:
2002

Citing 5
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Abstract

Let A, |A| ≤ n, be a subset of [0, 1]d, and let L(A, [0, 1]d, p) be the length of the minimal matching, the minimal spanning tree, or the traveling salesman problem on A with weight function w(e) = |e|p. In the case 1 ≤ p ≤ d, Yukich (Combinatorica 16 (1996) 575) obtained the asymptotic of αL(n, d, p) = max A⊆[0,1]d,|A| ≤ nL(A,[0,1]d,p). In this paper we extend his result to the whole range 0 ≤ p ≤ ∞.