NDLI: On the θ-coverage and connectivity of large random networks

Content Provider	ACM Digital Library
Author	Kumar, P. R. Xue, Feng
Abstract	Wireless planar networks have been used to model wireless networks in a tradition that dates back to 1961 to the work of E. N. Gilbert. Indeed, the study of connected components in wireless networks was the motivation for his pioneering work that spawned the modern field of continuum percolation theory. Given that node locations in wireless networks are not known, random planar modeling can be used to provide preliminary assessments of important quantities such as range, number of neighbors, power consumption, and connectivity, and issues such as spatial reuse and capacity. In this paper, the problem of connectivity based on nearest neighbors is addressed. The exact threshold function for θ-coverage is found for wireless networks modeled as $\textit{n}$ points uniformly distributed in a unit square, with every node connecting to its $φ\textit{n}$ nearest neighbors. A network is called θ-covered if every node, except those near the boundary, can find one of its $φ\textit{n}$ nearest neighbors in any sector of angle θ. For all θ ∈ (0, 2π), if $φ\textit{n}$ = (1 + δ) log 2π/2π-θ $\textit{n},$ it is shown that the probability of θ-coverage goes to one as $\textit{n}$ goes to infinity, for any δ > 0; on the other hand, if $φ\textit{n}$ = (1 - δ) log 2π/2π-θ $\textit{n},$ the probability of θ-coverage goes to zero. This sharp characterization of θ-coverage is used to show, via further geometric arguments, that the network will be connected with probability approaching one if $φ\textit{n}$ = (1 + δ) log2 $\textit{n}.$ Connections between these results and the performance analysis of wireless networks, especially for routing and topology control algorithms, are discussed.
Starting Page	2289
Ending Page	2299
Page Count	11
File Format	PDF
ISSN	10636692
DOI	10.1109/TIT.2006.874384
Volume Number	14
Issue Number	SI
Journal	IEEE/ACM Transactions on Networking (TON)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2006-06-01
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Ad hoc networks Connectivity Coverage Random geometric graphs Sensor networks Topology control Transmission power control Wireless networks
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Computer Networks and Communications Software Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

On the /spl theta/-coverage and connectivity of large random networks

Large Connectivity for Dynamic Random Geometric Graphs

Topological detection on wormholes in wireless ad hoc and sensor networks

Coverage by randomly deployed wireless sensor networks

Asymptotic connectivity in wireless ad hoc networks using directional antennas

Connectivity of ad hoc wireless networks: an alternative to graph-theoretic approaches

Asymptotic Connectivity in Wireless Ad Hoc Networks Using Directional Antennas

Algorithmic Models of Interference in Wireless Ad Hoc and Sensor Networks

Variable-Range Transmission Power Control in Wireless Ad Hoc Networks

On the θ-coverage and connectivity of large random networks

Similar Documents

On the /spl theta/-coverage and connectivity of large random networks

Large Connectivity for Dynamic Random Geometric Graphs

Topological detection on wormholes in wireless ad hoc and sensor networks

Coverage by randomly deployed wireless sensor networks

Asymptotic connectivity in wireless ad hoc networks using directional antennas

Connectivity of ad hoc wireless networks: an alternative to graph-theoretic approaches

Asymptotic Connectivity in Wireless Ad Hoc Networks Using Directional Antennas

Algorithmic Models of Interference in Wireless Ad Hoc and Sensor Networks

Variable-Range Transmission Power Control in Wireless Ad Hoc Networks

On the θ-coverage and connectivity of large random networks