One-dimensional geometric random graphs with nonvanishing densities II: a very strong zero-one law for connectivity

Authors:
Guang Han;Armand M. Makowski
Affiliations:
CTO Innovation Group, Nokia Siemens Networks, Arlington Heights, USA 60004;Department of Electrical and Computer Engineering, and the Institute for Systems Research, University of Maryland, College Park, USA 20742
Venue:
Queueing Systems: Theory and Applications
Year:
2012

Citing 8
Cited 0

On the connectivity of a random interval graph

Proceedings of the seventh international conference on Random structures and algorithms
A probabilistic analysis for the range assignment problem in ad hoc networks

MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks

IEEE Transactions on Mobile Computing
Threshold Functions for Random Graphs on a Line Segment

Combinatorics, Probability and Computing
The Critical Transmitting Range for Connectivity in Mobile Ad Hoc Networks

IEEE Transactions on Mobile Computing
The bin-covering technique for thresholding random geometric graph properties

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Sensitivity of critical transmission ranges to node placement distributions

IEEE Journal on Selected Areas in Communications - Special issue on stochastic geometry and random graphs for the analysis and designof wireless networks
One-dimensional geometric random graphs with nonvanishing densities: part I: a strong zero-one law for connectivity

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider a collection of n independent points which are distributed on the unit interval [0,1] according to some probability distribution function F. Two nodes communicate with each other if their distance is less than some given threshold value. When F admits a density f which is strictly positive on [0,1], we give conditions on f under which the property of graph connectivity for the induced geometric random graph obeys a very strong zero---one law when the transmission range is scaled appropriately with n large. The very strong critical threshold is identified. This is done by applying a version of the method of first and second moments.