This Article 
 Bibliographic References 
 Add to: 
Optimal Partitioning of Heterogeneous Traffic Sources in Mobile Communications Networks
March 1997 (vol. 46 no. 3)
pp. 312-325

Abstract—Given n heterogeneous traffic sources which generate multiple types of traffic among themselves, we consider the problem of finding a set of disjoint clusters to cover n traffic sources. The objective is to minimize the total communication cost for the entire system in the context that the intracluster communication is less expensive than the intercluster communication. Different from the general graph partitioning problem, our work takes into account the physical topology constraints of the linear arrangement of physical cells in highway cellular systems and the hexagonal mesh arrangement of physical cells in cellular systems. In our partitioning schemes, the optimal partitioning problem is transformed into an equivalent problem with a relative cost function, which generates the communication cost differences between the intracluster communications and the intercluster communications.

For highway cellular systems, we have designed an efficient optimal partitioning algorithm of O(mn2) by dynamic programming, where m is the number of clusters of n base stations. The algorithm also finds all the valid partitions in the same polynomial time, given the size constraint on a cluster and the total allowable communication cost for the entire system. For hexagonal cellular systems, we have developed four heuristics for the optimal partitioning based on the techniques of moving or interchanging boundary nodes between adjacent clusters. The heuristics have been evaluated and compared through experimental testing and analysis.

[1] B. Awerbuch and D. Peleg, “Concurrent Online Tracking of Mobile Users,” SIGCOM Symp. Communication Architectures and Protocols, Oct. 1991.
[2] B. Awerbuch and D. Peleg, "Sparse Partitions," Proc. 1990 IEEE 31th Ann. Symp. Foundations of Computer Science, pp. 503-513, 1990.
[3] B.S. Baker, "Approximation Algorithms for NP-Complete Problems on Planar Graphs," Proc. Symp. Foundation of Computer Science, pp. 265-273, 1983.
[4] A. Bar-Noy and I. Kessler, "Tracking Mobile Users in Wireless Communications Networks," Proc. INFOCOM '93, pp. 1,232-1,239, 1993.
[5] T.N. Bui and A. Peck, "Partitioning Planar Graphs," SIAM J. Computing, vol. 21, no. 2, pp. 203-215, 1992.
[6] T.N. Bui, S. Chaudhuri, F.T. Leighton, and M. Sipser, "Graph Bisection Algorithms with Good Average Case Behavior," Combinatorica, vol. 7, no. 2, pp. 171-191, 1987.
[7] L. Caccetta, "Graph Theory in Network Design and Analysis," Recent Studies in Graph Theory, V. R. Kulli, ed. Vishwa Int'l, 1989.
[8] E. Dahlhaus, D.S. Johnson, C.H. Papadimitriou, P.D. Seymour, and M. Yannakakis, “The Complexity of Multiway Cuts,” ACM Symp. Theory of Computing, pp. 241-251, 1992.
[9] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness.New York: W.H. Freeman, 1979.
[10] O. Goldschmidt and D.S. Hochbaum, "Polynomial Algorithm for the k-Cut Problem," Proc. 29th Ann. Symp. Foundations of Computer Science, pp. 444-451, 1988.
[11] T. Imielinski and B.R. Badrinath, "Querying Locations in Wireless Environments," Proc. Third Workshop Third Generation Wireless Information Networks, Apr. 1992.
[12] B.W. Kernighan and S. Lin, "An Efficient Heuristic Procedure for Partition Graphs," Bell System Technology, vol. 49, pp. 291-307, 1970.
[13] S. Kirkpatrick, C.D. Gelatt Jr., and M.P. Vecchi, "Optimization by Simulated Annealing," Science, vol. 220, pp. 671-680, 1993.
[14] E. Minieka, Optimization Algorithms for Networks and Graphs. Marcel Dekker, 1978.

Index Terms:
Optimal partition, dynamic programming, heuristics, highway cellular system, hexagonal cellular system, mobile communications network.
Kyungshik Lim, Yann-Hang Lee, "Optimal Partitioning of Heterogeneous Traffic Sources in Mobile Communications Networks," IEEE Transactions on Computers, vol. 46, no. 3, pp. 312-325, March 1997, doi:10.1109/12.580427
Usage of this product signifies your acceptance of the Terms of Use.