منابع مشابه
The weight of the shortest path tree
The minimal weight of the shortest path tree in a complete graph with independent and exponential (mean 1) random link weights, is shown to converge to a Gaussian distribution. We prove a conditional central limit theorem and show that the condition holds with probability converging to 1.
متن کاملOn the Clustered Shortest-Path Tree Problem
Given an n-vertex and m-edge non-negatively real-weighted graph G = (V, E, w), whose vertices are partitioned into a set of k clusters, a clustered network design problem on G consists of finding a (possibly optimal) solution to a given network design problem on G, subject to some additional constraint on its clusters. In this paper, we focus on the classic shortest-path tree problem and summar...
متن کاملThe weight-constrained shortest path problem
In this class project, we investigate certain aspects of the Weight Constrained Shortest Path Problem. The problem is known NP-Hard, but there are algorithms, both exact and approximate, that attempt to solve it. We analyze two of the important exact methods label setting on graphs and Lagrangean relaxation of the constraint, and evaluate how they perform with different graph sizes, and differe...
متن کاملWeight of a link in a shortest path tree and the Dedekind Eta function
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...
متن کاملInfluence of the link weight structure on the shortest path.
The shortest path tree rooted at a source to all other nodes is investigated in a graph with polynomial link weights tunable by the power exponent alpha. By varying alpha, different types of shortest path trees, in short alpha trees, appear. Especially, the alpha --> 0 regime that corresponds to heavily fluctuating link weights possesses a peculiar type of tree. The most important properties of...
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ژورنال
عنوان ژورنال: Random Structures and Algorithms
سال: 2007
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20141