The Diameter of Weighted Random Graphs

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...

THE DIAMETER OF WEIGHTED RANDOM GRAPHS By Hamed Amini and Marc

Distributed Algorithm for Shortest Path Problem in Undirected Graphs via Randomized Strategy

In this paper, we introduce a distributed algorithm for single source shortest path problem for undirected graphs. In this problem, we find the shortest path from a given source node to other nodes in the graph. We start with undirected unweighted graphs in which the shortest path is a path with minimum number of edges. Following, we modify the algorithm to find shortest path for weighted graph...

Critical Random Graphs and the Structure of a Minimum Spanning Treeb*

We consider the complete graph on n vertices whose edges are weighted by independent and identically distributed edge weights and build the associated minimum weight spanning tree. We show that if the random weights are all distinct, then the expected diameter of such a tree is (n1/3). This settles a question of Frieze and Mc-Diarmid (Random Struct Algorithm 10 (1997), 5–42). The proofs are bas...

Critical random graphs and the structure of a minimum spanning tree

We consider the complete graph on n vertices whose edges are weighted by independent and identically distributed edge weights and build the associated minimum weight spanning tree. We show that if the random weights are all distinct, then the expected diameter of such a tree is Θ(n). This settles a question of Frieze and McDiarmid [15]. The proofs are based on a precise analysis of the behaviou...