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
相关论文
共 50 条
  • [11] Quotients of values of the Dedekind Eta function
    Alkan, Emre
    Xiong, Maosheng
    Zaharescu, Alexandru
    MATHEMATISCHE ANNALEN, 2008, 342 (01) : 157 - 176
  • [12] Finding the Optimal Shortest Path Tree with Respect to Single Link Failure Recovery
    Li, Yueping
    Nie, Zhe
    Zhou, Xiaohong
    NCM 2008 : 4TH INTERNATIONAL CONFERENCE ON NETWORKED COMPUTING AND ADVANCED INFORMATION MANAGEMENT, VOL 1, PROCEEDINGS, 2008, : 412 - 415
  • [13] Fourier coefficients of powers of the Dedekind eta function
    Bernhard Heim
    Markus Neuhauser
    Florian Rupp
    The Ramanujan Journal, 2019, 48 : 1 - 11
  • [14] Values of the Dedekind eta function at quadratic irrationalities
    van der Poorten, A
    Williams, KS
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1999, 51 (01): : 176 - 224
  • [15] Fourier coefficients of powers of the Dedekind eta function
    Heim, Bernhard
    Neuhauser, Markus
    Rupp, Florian
    RAMANUJAN JOURNAL, 2019, 48 (01): : 1 - 11
  • [16] The analogue of the Dedekind eta function for CY manifolds I
    Bass, Jamey
    Todorov, Andrey
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2006, 599 : 61 - 96
  • [17] AN ELEMENTARY PROOF OF THE TRANSFORMATION FORMULA FOR THE DEDEKIND ETA FUNCTION
    Kong, Ze-Yong
    Teo, Lee-Peng
    arXiv, 2023,
  • [18] ON A LATTICE GENERALISATION OF THE LOGARITHM AND A DEFORMATION OF THE DEDEKIND ETA FUNCTION
    Betermin, Laurent
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2020, 102 (01) : 118 - 125
  • [19] On hecke operators and products of the dedekind eta-function
    Martin, Y
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1996, 322 (04): : 307 - 312
  • [20] Certain modular functions similar to the Dedekind eta function
    Horie, T
    Kanou, N
    ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2002, 72 (1): : 89 - 117
12345