Flooding and diameter in general weighted random graphs
نویسندگان
چکیده
منابع مشابه
Flooding in Weighted Random Graphs
In this paper, we study the impact of edge weights on distances in diluted random graphs. We interpret these weights as delays, and take them as i.i.d exponential random variables. We analyze the weighted flooding time defined as the minimum time needed to reach all nodes from one uniformly chosen node, and the weighted diameter corresponding to the largest distance between any pair of vertices...
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In this paper, we study the impact of the introduction of edge weights on the typical distances in a random graph and, in particular, on its diameter. Our main result consists of a precise asymptotic expression for the (edge) diameter of sparse random graphs on n vertices (under some standard regularity conditions) when the edge weights are i.i.d. exponential random variables of rate one.
متن کاملThe flooding time in random graphs
Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class Gp(N) of random graphs, the corresponding ßooding time is investigated. The ßooding time TN(p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the ßooding time TN(p) converges in distribution to the two-fold convolution Λ(2∗) of the Gumbel distribut...
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Extending some recent theorems of Klee and Larman, we prove rather sharp results about the diameter of a random graph. Among others we show that if d = d(n) > 3 and m = m(n) satisfy (log n)/d 3 log log n -> oo, 2rf_Imd'/'nd+x log n -» oo and dd~2md~l/nd — log n -» -oo then almost every graph with n labelled vertices and m edges has diameter d. About twenty years ago Erdös [7], [8] used random g...
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In the previous section we saw how we could use LP duality theory to develop an algorithm for the weighted matching problem in bipartite graphs. In this section, we’ll see how to extend that algorithm to handle general graphs. As in the unweighted case, blossom-shrinking plays a central role. However, in weighted graphs we will handle blossoms a bit differently. In particular, we will maintain ...
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2020
ISSN: 0021-9002,1475-6072
DOI: 10.1017/jpr.2020.45