article

Free access

The number of neighbors needed for connectivity of wireless networks

Authors:

P. R. KumarAuthors Info & Claims

Wireless Networks, Volume 10, Issue 2

Pages 169 - 181

https://doi.org/10.1023/B:WINE.0000013081.09837.c0

Published: 01 March 2004 Publication History

Abstract

Unlike wired networks, wireless networks do not come with links. Rather, links have to be fashioned out of the ether by nodes choosing neighbors to connect to. Moreover the location of the nodes may be random.The question that we resolve is: How many neighbors should each node be connected to in order that the overall network is connected in a multi-hop fashion? We show that in a network with n randomly placed nodes, each node should be connected to Θ(log n) nearest neighbors. If each node is connected to less than 0.074 log n nearest neighbors then the network is asymptotically disconnected with probability one as n increases, while if each node is connected to more than 5.1774 log n nearest neighbors then the network is asymptotically connected with probability approaching one as n increases. It appears that the critical constant may be close to one, but that remains an open problem.These results should be contrasted with some works in the 1970s and 1980s which suggested that the "magic number" of nearest neighbors should be six or eight.

References

[1]

{1} L. Kleinrock and J.A. Silvester, Optimum transmission radii for packet radio networks or why six is a magic number, in: Proc. of IEEE Nat. Telecommun. Conf. (December 1978) pp. 4.3.1-4.3.5.

[2]

{2} R. Mathar and J. Mattfeldt, Analyzing routing strategy NFP in multihop packet radio network on a line, IEEE Transactions on Communications 43(2-4) (1995) 977-988.

[3]

{3} J. Ni and S. Chandler, Connectivity properties of a random radio network, Proceedings of the IEE - Communications 141 (August 1994) 289-296.

[4]

{4} J.A. Silvester, On the spatial capacity of packet radio networks, Eng. Rep. UCLA-ENG-8021, Dept. Comput. Sci., School Eng. Appl. Sci., Univ. California, Los Angeles (March 1980).

[5]

{5} H. Takagi and L. Kleinrock, Optimal transmission ranges for randomly distributed packet radio terminals, IEEE Trans. Commun. 32 (1984) 246-257.

[6]

{6} T. Hou and V. Li, Transmission range control in multihop packet radio networks, IEEE Trans. Commun. 34 (January 1986) 38-44.

[7]

{7} B. Hajek, Adaptive transmission strategies and routing in mobile radio networks, in: Proceedings of the Conference on Information Sciences and Systems (March 1983) pp. 373-378.

[8]

{8} P. Gupta and P. Kumar, The capacity of wireless networks, IEEE Transactions on Information Theory 46 (March 2000) 388-404.

Digital Library

[9]

{9} T.K. Philips, S.S. Panwar and A.N. Tantawi, Connectivity properties of a packet radio network model, IEEE Transactions on Information Theory 35 (September 1989) 1044-1047.

[10]

{10} P. Gupta and P.R. Kumar, Critical power for asymptotic connectivity in wireless networks, in: Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, eds W.M. McEneany, G. Yin and Q. Zhang (Birkhäuser, Boston, MA, 1998) pp. 547-566.

[11]

{11} M.D. Penrose, The longest edge of the random minimal spanning tree, The Annals of Applied Probability 7(2) (1997) 340-361.

[12]

{12} B. Bollobás, Random Graphs (Academic Press, Orlando, FL, 1985).

[13]

{13} R. Meester and R. Roy, Continuum Percolation (Cambridge University Press, Cambridge, UK, 1996).

[14]

{14} H. Kesten, Percolation Theory for Mathematicians (Birkhäuser, Boston, MA, 1982).

[15]

{15} L. Booth, J. Bruck, M. Franceschetti and R. Meester, Covering algorithms, continuum percolation and the geometry of wireless networks, Preprint, http://www.paradise.caltech.edu/ETR.html (2001).

[16]

{16} M. Franceschetti, M. Cook and J. Bruck, A geometric theorem for approximate disk covering algorithms, Preprint, http://www.paradise.caltech.edu/ETR.html (2001).

[17]

{17} F. Avram and D. Bertsimas, On central limit theorems in geometrical probability, Annals of Applied Probability 3(4) (1993) 1033-1046.

[18]

{18} O. Häggström and R. Meester, Nearest neighbor and hard sphere models in continuum percolation, Random Structures and Algorithms 9 (1996) 295-315.

[19]

{19} S. Narayanaswamy, V. Kawadia, R.S. Sreenivas and P.R. Kumar, Power control in ad-hoc networks: Theory, architecture, algorithm and implementation of the COMPOW protocol, in: European Wireless Conference -- Next Generation Wireless Networks: Technologies, Protocols, Services and Applications, Florence, Italy (25-28 February 2002).

Cited By

Madin ZLawry JHunt EHong JPark J(2024)Collective Anomaly Perception During Multi-Robot Patrol: Constrained Interactions Can Promote Accurate ConsensusProceedings of the 39th ACM/SIGAPP Symposium on Applied Computing10.1145/3605098.3635975(630-637)Online publication date: 8-Apr-2024
https://dl.acm.org/doi/10.1145/3605098.3635975
ElSawy HZhaikhan AKishk MAlouini M(2024)A Tutorial-Cum-Survey on Percolation Theory With Applications in Large-Scale Wireless NetworksIEEE Communications Surveys & Tutorials10.1109/COMST.2023.333619426:1(428-460)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/COMST.2023.3336194
Zhang RYu CChen JFan CGao SKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Learning-based motion planning in dynamic environments using GNNs and temporal encodingProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602445(30003-30015)Online publication date: 28-Nov-2022
https://dl.acm.org/doi/10.5555/3600270.3602445
Show More Cited By

Index Terms

The number of neighbors needed for connectivity of wireless networks

Recommendations

Connectivity in cooperative wireless ad hoc networks
MobiHoc '08: Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing

Connectivity and capacity are two measures for the performance of mobile ad hoc networks that have been studied extensively under standard point-to-point physical layer assumptions. However, extensive recent research at the physical layer has ...
Connectionless protocol: a localised approach to wireless ad hoc networks

Most mobile ad hoc network's communication techniques need to discover routes and establish a connection before they can communicate. This strategy cannot robustly adapt to frequent unpredictable topology changes due to high mobility. Constant ...
Bloom filter based secure and anonymous DSR protocol in wireless ad hoc networks

Wireless ad hoc networks, especially in the hostile environment, are vulnerable to traffic analysis which allows the adversary to trace the routing messages and the sensitive data packets. Anonymity mechanism in ad hoc networks is a critical securing ...

Comments

Information & Contributors

Information

Published In

cover image Wireless Networks

Wireless Networks Volume 10, Issue 2

March 2004

120 pages

ISSN:1022-0038

Issue’s Table of Contents

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 March 2004

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

143
Total Citations
View Citations
2,502
Total Downloads

Downloads (Last 12 months)69
Downloads (Last 6 weeks)10

Reflects downloads up to 04 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Madin ZLawry JHunt EHong JPark J(2024)Collective Anomaly Perception During Multi-Robot Patrol: Constrained Interactions Can Promote Accurate ConsensusProceedings of the 39th ACM/SIGAPP Symposium on Applied Computing10.1145/3605098.3635975(630-637)Online publication date: 8-Apr-2024
https://dl.acm.org/doi/10.1145/3605098.3635975
ElSawy HZhaikhan AKishk MAlouini M(2024)A Tutorial-Cum-Survey on Percolation Theory With Applications in Large-Scale Wireless NetworksIEEE Communications Surveys & Tutorials10.1109/COMST.2023.333619426:1(428-460)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/COMST.2023.3336194
Zhang RYu CChen JFan CGao SKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Learning-based motion planning in dynamic environments using GNNs and temporal encodingProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602445(30003-30015)Online publication date: 28-Nov-2022
https://dl.acm.org/doi/10.5555/3600270.3602445
Yu CGao SRanzato MBeygelzimer ADauphin YLiang PVaughan J(2021)Reducing collision checking for sampling-based motion planning using graph neural networksProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3540588(4274-4289)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.5555/3540261.3540588
Solovey KSalzman OHalperin D(2018)New perspective on sampling-based motion planning via random geometric graphsInternational Journal of Robotics Research10.1177/027836491880295737:10(1117-1133)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1177/0278364918802957
Iqbal ZLee HNooshabadi S(2018)Highly Reliable Decision-Making Using Reliability Factor Feedback for Factory Condition Monitoring via WSNsWireless Communications & Mobile Computing10.1155/2018/80586242018Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.1155/2018/8058624
Shipu XYunsheng WYong LWeixiong RMingzhou MJingyin ZChenxi Z(2018)Research on WSN Routing Algorithm for Vegetable GreenhouseProceedings of the 2018 2nd High Performance Computing and Cluster Technologies Conference10.1145/3234664.3234668(37-42)Online publication date: 22-Jun-2018
https://dl.acm.org/doi/10.1145/3234664.3234668
Phanish DCoyle E(2018)Delay-efficient routing across high-throughput wireless network clusters2018 IEEE Wireless Communications and Networking Conference (WCNC)10.1109/WCNC.2018.8376995(1-6)Online publication date: 15-Apr-2018
https://dl.acm.org/doi/10.1109/WCNC.2018.8376995
Baskar SSarma Dhulipala V(2018)Collaboration of Trusted Node and QoS Based Energy Multi Path Routing Protocol for Vehicular Ad Hoc NetworksWireless Personal Communications: An International Journal10.1007/s11277-018-5965-1103:4(2833-2842)Online publication date: 1-Dec-2018
https://dl.acm.org/doi/10.1007/s11277-018-5965-1
Martínez JSong HDumas JLefebvre S(2017)Orthotropic k-nearest foams for additive manufacturingACM Transactions on Graphics10.1145/3072959.307363836:4(1-12)Online publication date: 20-Jul-2017
https://dl.acm.org/doi/10.1145/3072959.3073638
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents