Results 1 
6 of
6
Distributional limits for critical random graphs
 In preparation
, 2009
"... We consider the Erdős–Rényi random graph G(n, p) inside the critical window, that is when p = 1/n + λn −4/3, for some fixed λ ∈ R. Then, as a metric space with the graph distance rescaled by n −1/3, the sequence of connected components G(n, p) converges towards a sequence of continuous compact metri ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
We consider the Erdős–Rényi random graph G(n, p) inside the critical window, that is when p = 1/n + λn −4/3, for some fixed λ ∈ R. Then, as a metric space with the graph distance rescaled by n −1/3, the sequence of connected components G(n, p) converges towards a sequence of continuous compact metric spaces. The result relies on a bijection between graphs and certain marked random walks, and the theory of continuum random trees. Our result gives access to the answers to a great many questions about distances in critical random graphs. In particular, we deduce that the diameter of G(n, p) rescaled by n −1/3 converges in distribution to an absolutely continuous random variable with finite mean. Keywords: Random graphs, GromovHausdorff distance, scaling limits, continuum random tree, diameter. 2000 Mathematics subject classification: 05C80, 60C05.
Average update times for fullydynamic allpairs shortest paths
 Proceedings of the 19th International Symposium on Algorithms and Computation (ISAAC 2008), Gold Coast, Australia, 2008, LNCS 5369
"... Abstract We study the fullydynamic all pairs shortest path problem for graphs with arbitrary nonnegative edge weights. It is known for digraphs that an update of the distance matrix costs Õ(n2.75) 1 worstcase time [Thorup, STOC ’05] and Õ(n2) amortized time [Demetrescu and Italiano, J.ACM ’04] wh ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract We study the fullydynamic all pairs shortest path problem for graphs with arbitrary nonnegative edge weights. It is known for digraphs that an update of the distance matrix costs Õ(n2.75) 1 worstcase time [Thorup, STOC ’05] and Õ(n2) amortized time [Demetrescu and Italiano, J.ACM ’04] where n is the number of vertices. We present the first averagecase analysis of the undirected problem. For a random update we show that the expected time per update is bounded by O(n 4/3+ε) for all ε> 0.
A sharp threshold for minimum boundeddepth and boundeddiameter spanning trees and Steiner trees in random networks
, 2008
"... ..."
9. Bibliography............................................................................111. Team Research Scientist
"... c t i v it y e p o r t 2009 Table of contents 1. Team.................................................................................... 1 ..."
Abstract
 Add to MetaCart
c t i v it y e p o r t 2009 Table of contents 1. Team.................................................................................... 1
9. Bibliography............................................................................101. Team
"... c t i v it y e p o r t 2008 Table of contents 1. Team.................................................................................... 1 ..."
Abstract
 Add to MetaCart
c t i v it y e p o r t 2008 Table of contents 1. Team.................................................................................... 1
ProjectTeam Mascotte Méthodes Algorithmiques, Simulation et Combinatoire pour l’OpTimisation des
"... c t i v it y e p o r t 2009 Table of contents ..."