Let || ≤ n, be a subset of [0,1]d, and let L(,[0,1]d,p) be the length of the minimal matching, the minimal spanning tree, or the traveling salesman problem on 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⊃[0,1]d,≤n L(,[0,1]d,p). In this paper we extend his result to the whole range 0 < p < ∞.
Bibliographical noteFunding Information:
This work was supported by grant No. 1999-2-0577 from the interdisciplinary research program of the KOSEF, Com2MaC in POSTECH, and the BK21 project of the Department of Mathematics, Yonsei University. E-mail address: email@example.com (S. Lee).
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics