Wireless Personal Communications

, Volume 60, Issue 4, pp 611–633 | Cite as

Analysis of Heuristic Graph Partitioning Methods for the Assignment of Packet Control Units in GERAN

  • Matías TorilEmail author
  • Iñigo Molina-Fernández
  • Volker Wille
  • Chris Walshaw


Over the last few years, graph partitioning has been recognized as a suitable technique for optimizing cellular network structure. For example, in a recent paper, the authors proposed a classical graph partitioning algorithm to optimize the assignment of cells to Packet Control Units (PCUs) in GSM-EDGE Radio Access Network. Based on this approach, the quality of packet data services in a live environment was increased by reducing the number of cell re-selections between different PCUs. To learn more about the potential of graph partitioning in cellular networks, in this paper, a more sophisticated, yet computationally efficient, partitioning algorithm is proposed for the same problem. The new method combines multi-level refinement and adaptive multi-start techniques with algorithms to ensure the connectivity between cells under the same PCU. Performance assessment is based on an extensive set of graphs constructed with data taken from a live network. During the tests, the new method is compared with classical graph partitioning approaches. Results show that the proposed method outperforms classical approaches in terms of solution quality at the expense of a slight increase in computing time, while providing solutions that are easier to check by the network operator.


Graph partitioning Mobile Network Optimization Packet control unit 


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  1. 1.
    Lempiainen J., Manninen M. (2001) Radio interface system planning for GSM/GPRS/UMTS. Kluwer, DordrechtGoogle Scholar
  2. 2.
    Laiho J., Wacker A., Novosad T. (2002) Radio network planning and optimisation for UMTS. Wiley, West SussexGoogle Scholar
  3. 3.
    Mishra A. R. (2004) Fundamental of cellular network planning and optimisation. Wiley, West SussexCrossRefGoogle Scholar
  4. 4.
    Halonen T., Melero J., Romero J. (2002) GSM, GPRS and EDGE performance: Evolution toward 3G/UMTS. Wiley, ChichesterGoogle Scholar
  5. 5.
    Toril M., Wille V., Barco R. (2006) Optimization of the assignment of cells to packet control units in GERAN. IEEE Communications Letters 10(3): 219–221CrossRefGoogle Scholar
  6. 6.
    Schloegel K., Karypis G., Kumar V. (2000) Graph partitioning for high performance scientific simulations. In: Dongarra J., Foster I., Fox G., Kennedy K., White A. (eds) CRPC parallel computing handbook. Morgan Kaufmann, Los AltosGoogle Scholar
  7. 7.
    Miller, G. L., Teng, S.-H., Thurston, W., & Vavasis, S. A. (1993). Automatic mesh partitioning. In A. George, J. R. Gilbert, & J. Liu (Eds.), Sparse matrix computations: Graph theory issues and algorithms (An IMA Workshop Volume). Springer.Google Scholar
  8. 8.
    Kernighan B. W., Lin S. (1970) An efficient heuristic procedure for partitioning graphs. Bell System Technical Journal 49: 291–307zbMATHGoogle Scholar
  9. 9.
    Pothen A., Simon H. D., Liou K.-P. (1990) Partitioning sparse matrices with eigenvectors of graphs. SIAM Journal on Matrix Analysis and Applications 11(3): 430–452MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Hendrickson, B., & Leland, R. (1995). A multilevel algorithm for partitioning graphs. In Proceedings of 1995 ACM/IEEE Conference on Supercomputing. ACM Press.Google Scholar
  11. 11.
    Karypis G., Kumar V. (1998) Multilevel k-way partitioning scheme for irregular graphs. Journal of Parallel and Distributed Computing 48(1): 96–129MathSciNetCrossRefGoogle Scholar
  12. 12.
    Walshaw C., Cross M. (2000) Mesh partitioning: A multilevel balancing and refinement algorithm. SIAM Journal of Scientific Computing 22(1): 63–80MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Merchant A., Sengupta B. (1995) Assignment of cells to switches in PCS networks. IEEE/ACM Transactions on Networking 3(5): 521–526CrossRefGoogle Scholar
  14. 14.
    Saha D., Mukherjee A., Bhattacharjee P. S. (2000) A simple heuristic for assignment of cells to switches in a PCS network. Wireless Personal Communications 12: 209–224CrossRefGoogle Scholar
  15. 15.
    Pierre S., Houeto F. (2002) A tabu-search approach for assigning cells to switches in cellular mobile networks. Computer Communications 25(5): 465–478CrossRefGoogle Scholar
  16. 16.
    Demirkol I., Ersoy C., Caglayan M. U., Delic H. (2004) Location area planning and cell-to-switch assignment in cellular networks. IEEE Transactions on Wireless Communications 3(3): 880–890CrossRefGoogle Scholar
  17. 17.
    Plehn, J. (1995). The design of location areas in a GSM-network. In Proceedings of 45th IEEE vehicular technology conference (pp. 871–875).Google Scholar
  18. 18.
    Gondim, P. (1996). Genetic algorithms and location area partitioning problem in cellular networks. In Proceedings of 46th IEEE vehicular technology conference (pp. 1835–1838).Google Scholar
  19. 19.
    Bhattacharjee P. S., Saha D., Mukherjee A. (2004) An approach for location area planning in~a personal communication services network (PCSN). IEEE Transactions on Wireless Communications 3(4): 1176–1187CrossRefGoogle Scholar
  20. 20.
    Hagen L., Kahng A. (1997) Combining problem reduction and adaptive multi-start: A new technique for superior iterative partitioning. IEEE Transactions On Computer-Aided Design of Integrated Circuits and Systems 16(7): 709–717CrossRefGoogle Scholar
  21. 21.
    3GPP TS 05.08, Digital cellular telecommunications system (Phase 2); Radio subsystem link control (2000, November).Google Scholar
  22. 22.
    3GPP TS 43.129, Packet Switched Handover for GERAN A/Gb Mode; Stage 2 (2004, May).Google Scholar
  23. 23.
    Krishnan, R., Ramanathan, R., & Steentrup, M. (1999). Optimization algorithms for large self-structuring networks. In Proceedings of INFOCOM ’99 (Vol.~1, pp. 71–78).Google Scholar
  24. 24.
    Garey M., Johnson D. (1979) Computers and intractability: A guide to NP-completeness. W.H. Freeman and Company, CaliforniazbMATHGoogle Scholar
  25. 25.
    Goldschmidt O., Hochbaum D. S. (1994) A polynomial algorithm for the k-cut problem for fixed k. Mathematics of Operations Research 19(1): 24–37MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Gupta A. (1997) Fast and effective algorithms for graph partitioning and sparse matrix ordering. IBM Journal of Research and Development 41(1/2): 171–184CrossRefGoogle Scholar
  27. 27.
    Cormen T. H., Stein C., Rivest R. L., Leiserson C. E. (2001) Introduction to algorithms. McGraw-Hill Higher Education, New YorkzbMATHGoogle Scholar
  28. 28.
    Karypis G., Kumar V. (1998) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing 20(1): 359–392MathSciNetCrossRefGoogle Scholar
  29. 29.
    Ramanathan R., Steenstrup M. (1998) Hierarchically-organized, multi-hop mobile wireless networks for quality-of-service support. Mobile Networks and Applications 3(2): 101–119CrossRefGoogle Scholar
  30. 30.
    Boese K. D., Khang A., Muddu S. (1994) A new adaptive multi-start technique for combinatorial global optimizations. Operation Research Letters 16: 101–113zbMATHCrossRefGoogle Scholar
  31. 31.
    Bui T. N., Moon B. R. (1996) Genetic algorithm and graph partitioning. IEEE Transactions on Computers 45(7): 841–855MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Korosec P., Silc J., Robic B. (2004) Solving the mesh-partitioning problem with an ant-colony algorithm. Journal of Parallel Computing 30(5–6): 785–801CrossRefGoogle Scholar
  33. 33.
    Fiduccia, C., Mattheyses, R. (1982). A linear time heuristic for improving network partitions. In Proceedings of 19th ACM/IEEE design automation conference (pp. 175–181).Google Scholar
  34. 34.
    Walshaw C. (2004) Multilevel refinement for combinatorial optimisation problems. Annals of Operations Research 131: 325–372MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Toril M., Wille V. (2008) Optimization of the assignment of base stations to base station controllers in GERAN. IEEE Communications Letters 12(6): 477–479CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  • Matías Toril
    • 1
    Email author
  • Iñigo Molina-Fernández
    • 1
  • Volker Wille
    • 2
  • Chris Walshaw
    • 3
  1. 1.Communications Engineering DepartmentUniversity of MálagaMálagaSpain
  2. 2.Performance ServicesNokia Siemens NetworksHuntingdonUK
  3. 3.School of Computing and Mathematical SciencesUniversity of GreenwichLondonUK

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