Weight of a Link in a Shortest Path Tree and the Dedekind Eta Function

被引：0
|
作者：
Van Mieghem, Piet [1 ]
机构：
[1] Delft Univ Technol, Fac Elect Engn Math & Comp Sci, NL-2600 GA Delft, Netherlands
来源：
RANDOM STRUCTURES & ALGORITHMS | 2010年 / 36卷 / 03期
关键词：
link weights; shortest path; complete graph; Dedekind Eta function; RANDOM ASSIGNMENT PROBLEM; COMPLETE GRAPH; SPANNING TREE; LIMIT; SIZE;
D O I：
10.1002/rsa.20299
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
The weight of a randomly chosen link in the shortest path tree on the complete graph with exponential i.i.d. link weights is studied. The corresponding exact probability generating function and the asymptotic law are derived. As a remarkable coincidence, this asymptotic law is precisely the same as the distribution of the cost of one "job" in the random assignment problem. We also show that the asymptotic (scaled) maximum interattachment time to that shortest path tree, which is a uniform recursive tree, equals the square of the Dedekind Eta function, a central function in modular forms, elliptic functions, and the theory of partitions. (C) 2010 Wiley Periodicals, Inc. Random Struct. Alg., 36, 341-371, 2010
引用
收藏
页码：341 / 371
页数：31
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