On the giant component in wireless multi-hop networks

Authors:
Xiaoyuan Ta;Guoqiang Mao;Brian D. O. Anderson
Affiliations:
School of Electrical and Information Engineering, The University of Sydney and National ICT Australia Limited, Sydney, Australia;School of Electrical and Information Engineering, The University of Sydney and National ICT Australia Limited, Sydney, Australia;Research School of Information Sciences and Engineering, Australian National University and National ICT Australia Limited, Canberra, Australia
Venue:
WCNC'09 Proceedings of the 2009 IEEE conference on Wireless Communications & Networking Conference
Year:
2009

Citing 9
Cited 0

On the connectivity of a random interval graph

Proceedings of the seventh international conference on Random structures and algorithms
On k-connectivity for a geometric random graph

Random Structures & Algorithms
Geography-informed energy conservation for Ad Hoc routing

Proceedings of the 7th annual international conference on Mobile computing and networking
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
On the minimum node degree and connectivity of a wireless multihop network

Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Wireless Communications: Principles and Practice

Wireless Communications: Principles and Practice
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks

IEEE Transactions on Mobile Computing
Connectivity in wireless ad-hoc networks with a log-normal radio model

Mobile Networks and Applications
The k-Neighbors Approach to Interference Bounded and Symmetric Topology Control in Ad Hoc Networks

IEEE Transactions on Mobile Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we study the giant component, the largest component containing a non-vanishing fraction of nodes, in a wireless multi-hop network where n nodes are randomly and uniformly distributed in [0, 1]d (d = 1, 2) and any two nodes can communicate directly with each other iff their Euclidean distance is not larger than the transmission range r. We investigate the probability that the size of the giant component is at least a given threshold p with 0.5 p ≤ 1. For d = 1, we derive a closed-form analytical formula for this probability. For d = 2, we propose an empirical formula for this probability using simulations. In addition, we compare the transmission range required for having a connected network with the transmission range required for having a certain size giant component for d = 2. The comparison shows that a significant energy saving can be achieved if we only require most nodes (e.g. 95%) to be connected to the giant component rather than require all nodes to be connected. The results of this paper are of practical value in the design and analysis of wireless ad hoc networks and sensor networks.