Abstract
The minimum transmission radius R that preserves ad hoc network connectivity is equal to the longest edge in the minimum spanning tree. This article proposes to use the longest LMST (local MST, recently proposed message free approximation of MST) edge to approximate R using a wave propagation quazi-localized algorithm. Despite small number of additional edges in LMST with respect to MST, they can extend R by about 33% its range on networks with up to 500 nodes. We then prove that MST is a subset of LMST and describe a quazi-localized scheme for constructing MST from LMST. The algorithm eliminates LMST edges which are not in MST by a loop breakage procedure, which iteratively follows dangling edges from leaves to LMST loops, and breaks loops by eliminating their longest edges, until the procedure finishes at a single leader node, which then broadcasts R to other nodes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bose, P., Morin, P., Stojmenovic, I., Urrutia, J.: Routing with guaranteed delivery in ad hoc wireless networks. ACM Wireless Networks 7(6), 609–616 (2001)
Dai, Q., Wu, J.: Computation of Minimal Uniform Transmission Power in Ad Hoc Wireless Networks. In: 23 International Conference on Distributed Computing Systems Worksshops (ICDCSW 2003), Providence, Rhode Island, May 19-22 (2003)
Dulman, S., Havinga, P., Jurink, J.: Wave Leader Election Protocol for Wireless Sensor Networks. In: MMSA Workshop Delft The Netherlands (December 2002)
Li, N., Hou, J.C., Sha, L.: Design and Analysis of an MST-Based Topology Control Algorithm. In: Proc. INFOCOM 2003, San Francisco, USA (2003)
Li, X.-Y., Wang, Y., Wan, P.-J., Frieder, O.: Localized low weight graph and its applications in wireless ad hoc networks. In: INFOCOM (2004)
Narayanaswamy, S., Kawadia, S., Sreenivas, V., Kumar, P.: Power control in ad hoc networks: Theory, architecture, algorithm and implementation of compow protocol. In: Proc. European Wireless, pp. 156–162 (2002)
Penrose, M.: The longest edge of the random minimal spanning tree. The Annals of Applied Probability 7(2), 340–361 (1997)
Penrose, M.: A strong law for the longest edge of the minimal spanning tree. The Annals of Probability 27(1), 246–260 (1999)
Sanchez, M., Manzoni, P., Haas, Z.: Determination of critical transmission range in ad hoc networks. In: Proc. IEEE Multiaccess, Mobility and Teletraffic for Wireless Communication Conf., Venice, Italy (October 1999)
Santi, P., Blough, D.: The critical transmitting range for connectivity in sparse wireless ad hoc networks. IEEE Transactions on Mobile Computing 2(1), 1–15 (2003)
Althaus, E., Calinescu, G., Mandoiu, I., Prasad, S., Tchervenski, N., Zelikovsky, A.: Power Efficient Range Assignment in Ad-hoc Wireless Networks (submitted for publication)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ovalle-Martínez, F.J., Stojmenovic, I., García-Nocetti, F., Solano-González, J. (2004). Finding Minimum Transmission Radii for Preserving Connectivity and Constructing Minimal Spanning Trees in Ad Hoc and Sensor Networks. In: Ribeiro, C.C., Martins, S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24838-5_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-24838-5_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22067-1
Online ISBN: 978-3-540-24838-5
eBook Packages: Springer Book Archive