This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Self-Stabilizing Clustering of Tree Networks
April 2006 (vol. 55 no. 4)
pp. 416-427
ASCII Text
x 
 
Mehmet Hakan Karaata, "Self-Stabilizing Clustering of Tree Networks," IEEE Transactions on Computers, vol. 55, no. 4, pp. 416-427, April, 2006.
 
 
BibTex
x
 
@article{ 10.1109/TC.2006.60,
author = {Mehmet Hakan Karaata},
title = {Self-Stabilizing Clustering of Tree Networks},
journal ={IEEE Transactions on Computers},
volume = {55},
number = {4},
issn = {0018-9340},
year = {2006},
pages = {416-427},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2006.60},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Self-Stabilizing Clustering of Tree Networks
IS - 4
SN - 0018-9340
SP416
EP427
EPD - 416-427
A1 - Mehmet Hakan Karaata,
PY - 2006
KW - Clustering
KW - distributed systems
KW - fault tolerance
KW - p-centers
KW - self-stabilization
KW - tree.
VL - 55
JA - IEEE Transactions on Computers
ER -
 
In this paper, we present a self-stabilizing algorithm for finding clustering of tree networks on a distributed model of computation. Clustering is defined as the covering of the nodes of a network by subtrees such that the intersection of any two subtrees is at most a single node and the difference between the sizes of the largest and the smallest clusters is minimal. The proposed algorithm evenly partitions the network into nearly the same size clusters and places resources and services for each cluster at its clusterhead to minimize the cost of sharing resources and using the services. Due to being self-stabilizing, the algorithm can withstand transient faults and does not require initialization. The paper includes a correctness proof of the algorithm. It concludes with remarks on issues such as open and related problems and the application areas of the algorithm.

[1] A.D. Amis, R. Prakash, D. Huynh, and T. Vuong, “Max-Min d-Cluster Formation in Wireless Ad Hoc Networks,” Proc. INFOCOM, pp. 32-41, 2000.
[2] C. Chiang, H. Wu, W. Liu, and M. Gerla, “Routing in Clustered Multihop, Mobile Wireless Networks,” Proc. IEEE Singapore Int'l Conf. Networks, pp. 197-211, 1997.
[3] S.A. Cook, J. Pachl, and I.S. Pressman, “The Optimal Location of Replicas in a Network Using a Read-One-Write-All Policy,” Distributed Computing, vol. 15, pp. 57-66, 2002.
[4] P.M. Dearing and R.L. Francis, “A Minimax Location Problem on a Network,” Transportation Science, no. 8, pp. 333-343, 1974.
[5] S. Dolev, Self-Stabilization. Cambridge, Mass.: MIT Press, 2000. Ben-Gurion Univ. of the Negev, Israel.
[6] E. Erkut, R.L. Francis, and A. Tamir, “Distance-Constrained Multifacility Minimax Location Problems on Tree Networks,” Networks: An Int'l J., vol. 22, 1992.
[7] G.N. Frederickson, “Parametric Search and Locating Supply Centers in Trees,” Proc. Second Workshop Algorithms and Data Structures (WADS '91), F. Dehne, J.-R. Sack, and N. Santoro, eds., pp. 299-319, Aug. 1991.
[8] H. Garcia-Molina, “The Future of Data Replication,” Proc. IEEE Symp. Reliability in Distributed Software and Database Systems, pp. 13-19, Jan. 1986.
[9] A.J. Goldman, “Minimax Location of a Facility in a Network,” Transportation Science, vol. 6, no. 4, pp. 407-418, 1972.
[10] S.L. Hakimi, “Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph,” Operation Research, vol. 12, pp. 450-459, 1964.
[11] S.L. Hakimi, “Optimal Distribution of Switching Centers in a Communication Network and Some Related Problems,” Operations Research, vol. 13, pp. 462-475, 1965.
[12] S.L. Hakimi, E.F. Schmeichel, and J.G. Pierce, “On p-Centers in Networks,” Ibid, vol. 12, pp. 1-15, 1978.
[13] S. Halfin, “On Finding the Absolute and Vertex Centers of a Tree with Distances,” Ibid, vol. 8, pp. 75-77, 1974.
[14] G.Y. Handler, “Minimax Location of a Facility in an Undirected Tree Graph,” Ibid, vol. 7, pp. 287-293, 1973.
[15] G.Y. Handler, “Minimax Network Location Theory and Algorithms,” Technical Report Tech107, 1974.
[16] M.H. Karaata, “Stabilizing Ring Clustering,” J. Systems Architecture, vol. 50, no. 10, pp. 623-634, 2004.
[17] O. Kariv and S.L. Hakimi, “An Algorithmic Approach to Network Location Problems I: The $p$ -Centers,” SIAM J. Applied Math., vol. 37, pp. 513-538, 1979.
[18] E. Korach, D. Rotem, and N. Santoro, “Distributed Algorithms for Finding Centers and Medians in Networks,” ACM Trans. Programming Languages and Systems, vol. 6, no. 3, pp. 380-401, 1984.
[19] E. Minieka, “The m-Center Problem,” SIAM Rev., vol. 12, pp. 138-139, 1970.
[20] T.J. Lowe and R.L. Francis, “Convex Location Problems on Tree Networks,” Operations Research, p. 37, 1976.
[21] E. Royer and C. Toh, “A Review of Current Routing Protocols for Ad-Hoc Mobile Wireless Networks,” Mobile Wireless Networks, IEEE Personal Comm., Apr. 1999.
[22] E.J. Coyle and S. Bandyopadhyay, “An Energy Efficient Hierarchical Clustering Algorithm for Wireless Sensor Networks,” Proc. INFOCOM, 2003.
[23] T. Sheltami and H.T. Mouftah, “Clusterhead Controlled Token for Virtual Base Station On-Demand in Manets,” Proc. Int'l Conf. Distributed Computing Systems (ICDCS) Workshops, pp. 716-721, 2003.
[24] A. Tamir, D. P'erez-Brito, and J.A. Moreno-P'erez, “A Polynomial Algorithm for the $p$ -Centdian Problem on a Tree,” Networks, vol. 25, pp. 255-262, 1998.
[25] A. Tamir, “Improved Complexity Bounds for Center Location Problems on Networks by Using Dynamic Data Structures,” SIAM J. Discrete Math., vol. 1, no. 3, pp. 377-396, Aug. 1988.
[26] B.-F. Wang, “Finding r-Dominating Sets and p-Centers of Trees in Parallel,” IEEE Trans. Parallel and Distributed Systems, vol. 15, no. 8, pp. 687-698, 2004.

Index Terms:
Clustering, distributed systems, fault tolerance, p-centers, self-stabilization, tree.
Citation:
Mehmet Hakan Karaata, "Self-Stabilizing Clustering of Tree Networks," IEEE Transactions on Computers, vol. 55, no. 4, pp. 416-427, April 2006, doi:10.1109/TC.2006.60
Usage of this product signifies your acceptance of the Terms of Use.