TY - JOUR
T1 - Tail bound for the minimal spanning tree of a complete graph
AU - Kim, Jeong Han
AU - Lee, Sungchul
N1 - Copyright:
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 2003/10/1
Y1 - 2003/10/1
N2 - Suppose each edge of the complete graph Kn is assigned a random weight chosen independently and uniformly from the unit interval [0,1]. A minimal spanning tree is a spanning tree of Kn with the minimum weight. It is easy to show that such a tree is unique almost surely. This paper concerns the number Nn(α) of vertices of degree α in the minimal spanning tree of Kn. For a positive integer α, Aldous (Random Struct. Algorithms 1 (1990) 383) proved that the expectation of Nn(α) is asymptotically γ(α)n, where γ(α) is a function of α given by explicit integrations. We develop an algorithm to generate the minimal spanning tree and Chernoff-type tail bound for Nn(α).
AB - Suppose each edge of the complete graph Kn is assigned a random weight chosen independently and uniformly from the unit interval [0,1]. A minimal spanning tree is a spanning tree of Kn with the minimum weight. It is easy to show that such a tree is unique almost surely. This paper concerns the number Nn(α) of vertices of degree α in the minimal spanning tree of Kn. For a positive integer α, Aldous (Random Struct. Algorithms 1 (1990) 383) proved that the expectation of Nn(α) is asymptotically γ(α)n, where γ(α) is a function of α given by explicit integrations. We develop an algorithm to generate the minimal spanning tree and Chernoff-type tail bound for Nn(α).
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U2 - 10.1016/S0167-7152(03)00208-6
DO - 10.1016/S0167-7152(03)00208-6
M3 - Article
AN - SCOPUS:0042884136
VL - 64
SP - 425
EP - 430
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
IS - 4
ER -