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Annals of Operations Research

, Volume 153, Issue 1, pp 79–129 | Cite as

Models and solution techniques for frequency assignment problems

  • Karen I. Aardal
  • Stan P. M. van Hoesel
  • Arie M. C. A. Koster
  • Carlo Mannino
  • Antonio Sassano
Open Access
Article

Abstract

Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, wireless LANs, and military operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modeling ideas for each of the features of the problem, such as the handling of interference among radio signals, the availability of frequencies, and the optimization criterion.

This survey gives an overview of the models and methods that the literature provides on the topic. We present a broad description of the practical settings in which frequency assignment is applied. We also present a classification of the different models and formulations described in the literature, such that the common features of the models are emphasized. The solution methods are divided in two parts. Optimization and lower bounding techniques on the one hand, and heuristic search techniques on the other hand. The literature is classified according to the used methods. Again, we emphasize the common features, used in the different papers. The quality of the solution methods is compared, whenever possible, on publicly available benchmark instances.

Keywords

Frequency assignment Channel assignment Wireless networks Mathematical optimization models Exact methods Heuristics 

References

  1. Aardal, K. I., Hipolito, A., van Hoesel, C. P. M., & Jansen, B. (1996). A branch-and-cut algorithm for the frequency assignment problem. Research Memorandum 96/011, Maastricht University. Google Scholar
  2. Aardal, K. I., Hurkens, C. A. J., Lenstra, J. K., & Tiourine, S. R. (2002). Algorithms for radio link frequency assignment: The CALMA project. Operations Research, 50(6), 968–980. CrossRefGoogle Scholar
  3. Aardal, K. I., van Hoesel, C. P. M., Koster, A. M. C. A., Mannino, C., & Sassano, A. (2003). Models and solution techniques for the frequency assignment problem. 4OR, 1(4), 261–317. Google Scholar
  4. Abril, J., Comellas, F., Cortés, A., Ozón, J., & Vaquer, M. (2000). A multi-agent system for frequency assignment in cellular radio networks. IEEE Transactions on Vehicular Technology, 49(5), 1558–1565. CrossRefGoogle Scholar
  5. Adjakplé, P. M., & Jaumard, B. (1997). Greedy and tabu search heuristics for channel block assignment in cellular systems. Technical Report G-97-45, École Polytechnique de Montréal, July 1997. Google Scholar
  6. Al-Khaled, F. S. (1998). Optimal radio channel assignment through the new binary dynamic simulated annealing algorithm. International Journal of Communication Systems, 11, 327–336. CrossRefGoogle Scholar
  7. Allen, S. M., Smith, D. H., & Hurley, S. (1999). Lower bounding techniques for frequency assignment. Discrete Mathematics, 197–198, 41–52. Google Scholar
  8. Allen, S. M., Dunkin, N., Hurley, S., & Smith, D. (1998). Frequency assignment problems: Benchmarks and lower bounds. Technical report, University of Glamorgan. URL http://www.glam.ac.uk/sotschool/doms/Research/Fap2last.pdf.
  9. Alouf, S., Altman, E., Galtier, J., Lalande, J.-F., & Touati, C. (2005). An algorithm for satellite bandwidth allocation. In Proceedings of IEEE infocom 2005 (Vol. 1, pp. 560–571). Google Scholar
  10. Anderson, L. G. (1973). A simulation study of some dynamic channel assignment algorithms in a high capacity mobile telecommunications system. IEEE Transactions on Communications, 21, 1294–1301. CrossRefGoogle Scholar
  11. Avenali, A., Mannino, C., & Sassano, A. (2002). Minimizing the span of d-walks to compute optimum frequency assignments. Mathematical Programming, 91(2), 357–374. Previously published as technical report 04-00, DIS-Università di Roma “La Sapienza”, Rome, Italy. CrossRefGoogle Scholar
  12. Baybars, I. (1982). Optimal assignment of broadcasting frequencies. European Journal of Operations Research, 9, 257–263. CrossRefGoogle Scholar
  13. Beckmann, D., & Killat, U. (1999a). Frequency planning with respect to interference minimization in cellular radio networks. Technical Report TD(99) 032 COST 259, Vienna, Austria, January 1999. Google Scholar
  14. Beckmann, D., & Killat, U. (1999b). A new strategy for the application of genetic algorithms to the channel-assignment problem. IEEE Transactions on Vehicular Technology, 48(4), 1261–1269. July 1999. CrossRefGoogle Scholar
  15. Björklund, P., Värbrand, P., & Yuan, D. (2005). Optimal frequency planning in mobile networks with frequency hopping. Computers and Operations Research, 32, 169–186. CrossRefGoogle Scholar
  16. Bodlaender, H. L. (1997). Treewidth: Algorithmic techniques and results. Lecture notes in computer science: Vol. 1295, Proceedings 22nd international symposium on mathematical foundations of computer science, MFCS’97 (pp. 29–36). Google Scholar
  17. Borgne, L. (1994). Automatic frequency assignment for cellular networks using local search heuristics. Master’s thesis, Uppsala University. Google Scholar
  18. Borndörfer, R., Eisenblätter, A., Grötschel, M., & Martin, A. (1998a). Frequency assignment in cellular phone networks. Annals of Operations Research, 76, 73–93. CrossRefGoogle Scholar
  19. Borndörfer, R., Eisenblätter, A., Grötschel, M., & Martin, A. (1998b). The orientation model for frequency assignment problems. Technical Report TR 98-01, Konrad-Zuse-Zentrum für Informationstechnik Berlin. Google Scholar
  20. Bouju, A., Boyce, J. F., Dimitropoulos, C. H. D., Vom Scheidt, G., & Taylor, J. G. (1995a). Tabu search for the radio links frequency assignment problem. In Applied decision technologies (ADT’95), London. Google Scholar
  21. Bouju, A., Boyce, J. F., Dimitropoulos, C. H. D., Vom Scheidt, G., Taylor, J. G., Likas, A., Papageorgiou, G., & Stafylopatis, A. (1995b). Intellegent search for the radio links frequency assignment problem. In International conference for digital signal processing (DSP’95), Limassol, Cypres. Google Scholar
  22. Box, F. (1978). A heuristic technique for assigning frequencies to mobile radio nets. IEEE Transactions on Vehicular Technology, 27, 57–74. Google Scholar
  23. Brélaz, D. (1979). New methods to color the vertices of a graph. Communications of the ACM, 22, 251–256. CrossRefGoogle Scholar
  24. Cabon, B., De Givry, S., Lobjois, L., Schiex, T., & Warners, J. P. (1999). Benchmarks problems: Radio link frequency assignment. Constraints, 4, 79–89. CrossRefGoogle Scholar
  25. Calamoneri, T. (Ed.). (2006). International Journal of Mobile Network Design and Innovation, 1, 2. CrossRefGoogle Scholar
  26. CALMA website. (1995). EUCLID CALMA project. Publications and instances available at FTP Site: ftp://ftp.win.tue.nl/pub/techreports/CALMA/.
  27. Capone, A., & Trubian, M. (1999). Channel assignment problem in cellular systems: a new model and a tabu search algorithm. IEEE Transactions on Vehicular Technology, 48(4), 1252–1260. CrossRefGoogle Scholar
  28. Carlsson, M., & Grindal, M. (1993). Automatic frequency assignment for cellular telephones using constraint satisfaction techniques, In Proceedings of the tenth international conference on logic programming (pp. 648–665). Google Scholar
  29. Castelino, D. J., Hurley, S., & Stephens, N. M. (1996). A tabu search algorithm for frequency assignment. Annals of Operations Research, 63, 301–319. CrossRefGoogle Scholar
  30. Chang, K.-N., & Kim, S. (1997). Channel allocation in cellular radio networks. Computers and Operations Research, 24(9), 849–860. CrossRefGoogle Scholar
  31. Christofides, N. (1975). Graph theory: An algorithmic approach. London: Academic. Google Scholar
  32. Colombo, G. (2006). A genetic algorithm for frequency assignment with problem decomposition. International Journal of Mobile Network Design and Innovation, 1(2), 102–112. CrossRefGoogle Scholar
  33. Cooper, M. C., de Givry, S., & Schiex, T. (2007). Optimal soft arc consistency, In Proceedings of international joint conference on artificial intelligence (IJCAI’2007), Hyderabad, India. Google Scholar
  34. Correia, L. M. (Ed.). (2001). Wireless flexible personalized communications—COST 259: European co-operation in mobile radio research. New York: Wiley. COST Action 259—Final Report. Google Scholar
  35. Costa, D. (1993). On the use of some known methods for t-colourings of graphs. Annals of Operations Research, 41, 343–358. CrossRefGoogle Scholar
  36. Cozzens, M. B., & Roberts, F. S. (1982). T-colorings of graphs and the channel assignment problem. Congressus Numerantium, 35, 191–208. Google Scholar
  37. Crisan, C., & Mühlenbein, H. (1998). The breeder genetic algorithm for frequency assignment. In Lecture notes in computer science (Vol. 1498, pp. 897–906). Google Scholar
  38. Crompton, W., Hurley, S., & Stephens, N. M. (1994). A parallel genetic algorithm for frequency assignment problems. In Proceedings IMACS/IEEE international symposium on signal processing, robotics and neural networks (pp. 81–84). Lille, France, April 1994. Google Scholar
  39. Cuppini, M. (1994). A genetic algorithm for channel assignment problems. European Transactions on Telecommunications and Related Technologies, 5, 285–294. CrossRefGoogle Scholar
  40. Del Re, E., Fantacci, R., & Ronga, L. (1996). A synamic channel allocation technique based on Hopfield neural networks. IEEE Transactions on Vehicular Technology, 45, 26–32. CrossRefGoogle Scholar
  41. Dorne, R., & Hao, J.-K. (1995). An evolutionary approach for frequency assignment in cellular radio networks. In IEEE international conference on evolutionary computing, Perth, Australia. Google Scholar
  42. Dorne, R., & Hao, J.-K. (1996). Constraint handling in evolutionary search: A case study of the frequency assignment. In Lecture notes in computer science (Vol. 1141, pp. 801–810). Google Scholar
  43. Dorne, R., & Hao, J.-K. (1998). A new genetic local search algorithm for graph coloring. In Lecture notes in computer science (Vol. 1498, pp. 745–754). Google Scholar
  44. Dunkin, N., & Allen, S. M. (1997). Frequency assignment problems: Representations and solutions. Technical Report CSD-TR-97-14 Royal Holloway, University of London. Google Scholar
  45. Dunkin, N., Bater, J., Jeavons, P., & Cohen, D. (1998). Towards high order constraint representations for the frequency assignment problem. Technical Report CSD-TR-98-05, Royal Holloway University of London. Google Scholar
  46. Dupont, A., Alvernhe, E., & Vasquez, M. (2004). Efficient filtering and tabu search on a consistent neighbourhood for the frequency assignment problem with polarisation. Annals of Operations Research, 130, 179–198. CrossRefGoogle Scholar
  47. Duque-Antón, M., Kunz, D., & Rüber, B. (1993). Channel assignment for cellular radio using simulated annealing. IEEE Transactions on Vehicular Technology, 42, 14–21. CrossRefGoogle Scholar
  48. Eisenblätter, A. (2001). Frequency assignment in GSM networks: Models, heuristics, and lower bounds. PhD thesis, Technische Universität Berlin, Berlin, Germany, 2001. Google Scholar
  49. Eisenblätter, A. (2002). The semidefinite relaxation of the k-partition polytope is strong. In W. J. Cook & A. S. Schulz (Eds.), Lecture notes in computer science: Vol. 2337. Proceedings of the 9th conference on integer programming and combinatorial optimization (IPCO’02) (pp. 273–290). Berlin: Springer. CrossRefGoogle Scholar
  50. Eisenblätter, A., Grötschel, M., & Koster, A. M. C. A. (2002). Frequency assignment and ramifications of coloring. Discussiones Mathematicae Graph Theory, 22, 51–88. Google Scholar
  51. Eisenblätter, A., Geerdes, H.-F., & Siomina, I. (2006). Integrated access point placement and channel assignment for wireless LANs in an indoor office environment. Technical Report 346 Matheon Berlin, Germany. URL http://www.matheon.de. To appear in Proceedings of IEEE WoWMoM, Helsinki, Finland, 2007.
  52. Erdős, P., Rubin, A. L., & Taylor, H. (1979). Choosability in graphs. Congressus Numerantium, 26, 125–157. Google Scholar
  53. FAP (2006). Frequency assignment problems, December 2006. URL http://www.fap.ema.fr/.
  54. FAP web (2000–2007). A website devoted to frequency assignment. URL http://fap.zib.de. Maintained by A. Eisenblätter & A. M. C. A. Koster.
  55. Fischetti, M., Lepschy, C., Minerva, G., Romanin-Jacur, G., & Toto, E. (2000). Frequency assignment in mobile radio systems using branch-and-cut techniques. European Journal of Operational Research, 123, 241–255. Previously published as technical report of the Universita di Padova. CrossRefGoogle Scholar
  56. Funabiki, N., & Takefuji, Y. (1992). A neural network parallel algorithm for channel assignment problems in cellular radio networks. IEEE Transactions on Vehicular Technology, 41, 430–437. CrossRefGoogle Scholar
  57. Galinier, P., & Hao, J.-K. (2004). A general approach for constraint solving by local search. Journal of Mathematical Modelling and Algorithms, 3, 73–88. CrossRefGoogle Scholar
  58. Galinier, P., Gendreau, M., Soriano, P., & Bisaillon, S. (2005). Solving the frequency assignment problem with polarization by local search and tabu. 4OR: A Quarterly Journal of Operations Research, 3, 59–78. Google Scholar
  59. Gamst, A. (1986). Some lower bounds for a class of frequency assignment problems. IEEE Transactions on Vehicular Technology, 35, 8–14. Google Scholar
  60. Gamst, A. (1991). Application of graph theoretical methods to GSM radio network planning. In Proceedings of IEEE international symposium on circuits and systems (Vol. 2, pp. 942–945). Google Scholar
  61. Gamst, A., & Rave, W. (1982). On frequency assignment in mobile automatic telephone systems. In Proceedings of GLOBECOM’82. New York: IEEE. Google Scholar
  62. Giortzis, A. I., & Turner, L. F. (1997). Application of mathematical programming to the fixed channel assignment problem in mobile radio networks. IEE Proceedings—Communications, 144, 257–264. Google Scholar
  63. Graham, J. S., Montemanni, R., Moon, J. N. J., & Smith, D. H. (2007, to appear). Frequency assignment, multiple interference and binary constraints, ACM Wireless Networks. Google Scholar
  64. Hale, W. K. (1980). Frequency assignment: Theory and applications. Proceedings of the IEEE, 68, 1497–1514. CrossRefGoogle Scholar
  65. Hao, J.-K., & Dorne, R. (1996). Study of genetic search for the frequency assignment problem. In Lecture notes in computer science (Vol. 1063, pp. 333–344). Google Scholar
  66. Hao, J.-K., & Perrier, L. (1999). Tabu search for the frequency assignment problem in cellular radio networks. Technical Report LGI2P, EMA-EERIE, Parc Scientifique Georges Besse, Nimes, France. Google Scholar
  67. Hao, J.-K., Dorne, R., & Galinier, P. (1998). Tabu search for frequency assignment in mobile radio networks. Journal of Heuristics, 4, 47–62. CrossRefGoogle Scholar
  68. Hellebrandt, M., & Heller, H. (2000). A new heuristic method for frequency assignment. Technical Report TD(00) 003 COST 259 Valencia, Spain, January 2000. Google Scholar
  69. Hertz, A., Schindl, D., & Zufferey, N. (2005). Lower bounding and tabu search procedures for the frequency assignment problem with polarization constraints. 4OR: A Quarterly Journal of Operations Research, 3, 139–161. Google Scholar
  70. Hurley, S. (2002). Planning effective cellular mobile radio networks. IEEE Transactions on Vehicular Technology, 12(5), 243–253. CrossRefGoogle Scholar
  71. Hurley, S., & Smith, D. H. (2002). Meta-heuristics and channel assignment. In R. Leese & S. Hurley (Eds.), Methods and algorithms for radio channel assignment. Oxford: Oxford University Press, Chap. 3. Google Scholar
  72. Hurley, S., Smith, D. H., & Thiel, S. U. (1997). FASoft: A system for discrete channel frequency assignment. Radio Science, 32, 1921–1939. CrossRefGoogle Scholar
  73. Jaimes-Romero, F. J., Munoz-Rodriguez, D., & Tekinay, S. (1996). Channel assignment in cellular systems using genetic algorithms. In Proceedings of the 46th IEEE vehicular technology conference (pp. 741–745), Atlanta, USA. Google Scholar
  74. Janssen, J., & Kilakos, K. (1999). An optimal solution to the “Philadelphia” channel assignment problem. IEEE Transactions on Vehicular Technology, 48(3), 1012–1014. Previously published as report CDAM-96-16 London School of Economics. CrossRefGoogle Scholar
  75. Janssen, J., & Wentzell, T. (2000). Lower bounds from tile covers for the channel assignment problem. Technical Report G-2000-09 GERAD, HEC, Montreal, Canada. Google Scholar
  76. Jaumard, B., Marcotte, O., & Meyer, C. (1998). Estimation of the quality of cellular networks using column generation techniques. Technical Report G-98-02 Ecole Polytechnique de Montréal, January 1998. Google Scholar
  77. Jaumard, B., Marcotte, O., & Meyer, C. (1999). Mathematical models and exact methods for channel assignment in cellular networks. In B. Sansáo & P. Soriano (Eds.), Telecommunications network planning (pp. 239–255). Boston: Kluwer Academic, Chap. 13. Google Scholar
  78. Jaumard, B., Marcotte, O., Meyer, C., & Vovor, T. (2002). Comparison of column generation models for channel assignment in cellular networks. Discrete Applied Mathematics, 118, 299–322. Previously published as technical report of Ecole Polytechnique de Montréal, November 1998. CrossRefGoogle Scholar
  79. Kalvenes, J., Kennington, J., & Olinick, E. (2005). Hierarchical cellular network design with channel allocation. European Journal of Operational Research, 160, 3–18. CrossRefGoogle Scholar
  80. Kapsalis, A., Chardaire, P., Rayward-Smith, V. J., & Smith, G. D. (1995). The radio link frequency assignment problem: A case study using genetic algorithms. In Lecture notes on computer science (Vol. 993, pp. 117–131). Google Scholar
  81. Karmarkar, N., Resende, M. G. C., & Ramakrishnan, K. G. (1991). An interior point algorithm to solve computationally difficult set covering problems. Mathematical Programming, 52, 597–618. CrossRefGoogle Scholar
  82. Katzela, I., & Naghshineh, M. (1996). Channel assignment schemes for cellular mobile telecommunication systems. Personal Communications Magazine, 3(3), 10–31. CrossRefGoogle Scholar
  83. Kazantzakis, M. G., Demestichas, P. P., & Anagnostou, M. E. (1995). Optimum frequency reuse in mobile telephone systems. International Journal of Communications Systems, 8, 185–190. Google Scholar
  84. Kim, J.-S., Park, S., Dowd, P., & Nasrabadi, N. (1996). Cellular radio channel assignment using a modified Hopfield network. IEEE Transactions on Vehicular Technology, 46(4), 957–967. CrossRefGoogle Scholar
  85. Knälmann, A., & Quellmalz, A. (1994). Solving the frequency assignment problem with simulated annealing. IEE Conference Publication, 396, 233–240. Google Scholar
  86. Kolen, A. W. J. (2007). A genetic algorithm for frequency assignment. Statistica Neerlandica, 61(1), 4–15. CrossRefGoogle Scholar
  87. Kolen, A. W. J., van Hoesel, C. P. M., & van der Wal, R. (1994). A constraint satisfaction approach to the radio link frequency assignment problem. Technical Report 2.2.2 EUCLID CALMA project. Google Scholar
  88. Koller, A. E., & Noble, S. D. (2004). Domination analysis of greedy heuristics for the frequency assignment problem. Discrete Mathematics, 275, 331–338. CrossRefGoogle Scholar
  89. Koster, A. M. C. A. (1999). Frequency assignment—models and algorithms. PhD thesis, Maastricht University. Google Scholar
  90. Koster, A. M. C. A., van Hoesel, C. P. M., & Kolen, A. W. J. (1998). The partial constraint satisfaction problem: Facets and lifting theorems. Operations Research Letters, 23(3–5), 89–97. CrossRefGoogle Scholar
  91. Koster, A. M. C. A., van Hoesel, C. P. M., & Kolen, A. W. J. (2001). Lower bounds for minimum interference frequency assignment problems. Ricerca Operativa, 30(94–95), 101–116. Google Scholar
  92. Koster, A. M. C. A., van Hoesel, C. P. M., & Kolen, A. W. J. (2002). Solving partial constraint satisfaction problems with tree decomposition. Networks, 40(3), 170–180. CrossRefGoogle Scholar
  93. Král, D. (2005). An exact algorithm for the channel assignment problem. Discrete Applied Mathematics, 145, 326–331. CrossRefGoogle Scholar
  94. Kunz, D. (1991). Channel assignment for cellular radio using neural networks. IEEE Transactions on Vehicular Technology, 40, 188–193. CrossRefGoogle Scholar
  95. Lai, W. K., & Coghill, G. G. (1996). Channel assignment through evolutionary optimization. IEEE Transactions on Vehicular Technology, 45, 91–95. CrossRefGoogle Scholar
  96. Lee, Y., Kim, K., & Choi, Y. (2002). Optimization of AP placement and channel assignment in wireless LANs. In Proceedings of LCN’02, Tampa, FL. Google Scholar
  97. Leese, R., & Hurley, S. (Eds.) (2002). Methods and algorithms for radio channel assignment. Oxford lecture series in mathematics and its applications. Oxford: Oxford University Press. Google Scholar
  98. Leung, K. K., & Kim, B.-J. (2003). Frequency assignment for IEEE 802.11 wireless networks. In Proceedings of VTC 2003-Fall, Orlando, FL. Google Scholar
  99. Ling, X., & Yeung, K. L. (2005). Joint access point placement and channel assignment for 802.11 wireless LANs. In Proceedings of WCNC 2005, New Orleans, LA. Google Scholar
  100. Maniezzo, V., & Carbonaro, A. (2000). An ants heuristic for the frequency assignment problem. Future Generation Computer Systems, 16, 927–935. CrossRefGoogle Scholar
  101. Maniezzo, V., & Montemanni, R. (2000). An exact algorithm for the min-interference frequency assignment problem. Technical Report WP-CO0003 Scienze dell’Informazione, University of Bologna, Cesena, Italy. Google Scholar
  102. Mannino, C., & Sassano, A. (2003). An enumerative algorithm for the frequency assignment problem. Discrete Applied Mathematics, 129(1), 155–169. CrossRefGoogle Scholar
  103. Mannino, C., Oriolo, G., & Sassano, A. (2000). Weighted stable set problem in k-thin graphs. Technical Report 09–00 Universitá di Roma “La Sapienza”. Google Scholar
  104. Mathar, R., & Mattfeldt, J. (1993). Channel assignment in cellular radio networks. IEEE Transactions on Vehicular Technology, 42, 647–656. CrossRefGoogle Scholar
  105. Mathar, R., & Schmeink, M. (2001). Optimal base station positioning and channel assignment for 3G mobile networks by integer programming. Annals of Operations Research, 107, 225–236. CrossRefGoogle Scholar
  106. Mehrotra, A., & Trick, M. A. (1996). A column generation approach for graph coloring. INFORMS Journal on Computing, 8, 344–354. CrossRefGoogle Scholar
  107. Metzger, B. H. (1970). Spectrum management technique. Presentation at 38th National ORSA meeting, Detroit, MI. Google Scholar
  108. Mishra, A., Banerjee, S., & Arbaugh, W. (2005). Weighted coloring based channel assignment for wlans. ACM SIGMOBILE Mobile Computing and Communications Review, 9(3), 19–31. CrossRefGoogle Scholar
  109. Montemanni, R., Smith, D. H., & Allen, S. M. (2002a). Lower bounds for fixed spectrum frequency assignment. Annals of Operations Research, 107(1–4), 237–250. Google Scholar
  110. Montemanni, R., Smith, D. H., & Allen, S. M. (2002b). An ANTS algorithm for the minimum-span frequency-assignment problem with multiple interference. IEEE Transactions on Vehicular Technology, 15(5), 949–953. CrossRefGoogle Scholar
  111. Montemanni, R., Moon, J. N. J., & Smith, D. H. (2003). An improved tabu search algorithm for the fixed spectrum frequency assignment problem. IEEE Transactions on Vehicular Technology, 52(4), 891–901. CrossRefGoogle Scholar
  112. Montemanni, R., Smith, D. H., & Allen, S. M. (2004). An improved algorithm to determine lower bounds for the fixed spectrum frequency assignment problem. European Journal of Operational Research, 156, 736–751. CrossRefGoogle Scholar
  113. Moon, J. N. J., Hughes, L. A., & Smith, D. H. (2005). Assignment of frequency lists in frequency hopping networks. IEEE Transactions on Vehicular Technology, 54(3), 1147–1159. CrossRefGoogle Scholar
  114. Murphey, R. A., Pardalos, P. M., & Resende, M. G. C. (1999). Frequency assignment problems. In D.-Z. Du & P. M. Pardalos (Eds.), Handbook of combinatorial optimization, Supplement Volume A. Dordrecht: Kluwer Academic. Google Scholar
  115. Nemhauser, G. L., & Wolsey, L. A. (1988). Integer and combinatorial optimization. New York: Wiley. Google Scholar
  116. Ngo, C. Y., & Li, V. O. K. (1998). Fixed channel assignment in cellular radio networks using a modified genetic algorithm. IEEE Transactions on Vehicular Technology, 47, 163–171. CrossRefGoogle Scholar
  117. Nielsen, T., & Wigard, J. (2000). Performance enhancements in a frequency hopping GSM network. Dordrecht: Kluwer Academic. ISBN: 0 7923 7819 9. Google Scholar
  118. Padberg, M. (1989). The boolean quadric polytope: Some characteristics, facets and relatives. Mathematical Programming, 45, 139–172. CrossRefGoogle Scholar
  119. Palpant, M., Artigues, C., & Michelon, P. (2002). A heuristic for solving the frequency assignment problem. In XI Latin–Iberian–American congress of operations research (CLAIO 2002). Google Scholar
  120. Papadimitriou, C. H., & Steiglitz, K. (1982). Combinatorial optimization: Algorithms and complexity. New Jersey: Prentice-Hall. Google Scholar
  121. Park, T., & Lee, C. Y. (1996). Application of the graph coloring algorithm to the frequency assignment problem. Journal of the Operations Research Society of Japan, 39, 258–265. Google Scholar
  122. Petford, A., & Welsh, D. (1989). A randomised 3-colouring algorithm. Discrete Mathematics, 74, 253–261. CrossRefGoogle Scholar
  123. Quellmalz, A., Knälmann, A., & Müller, B. (1995). Efficient frequency assignment with simulated annealing. IEE Conference Publication, 407(2), 301–304. Google Scholar
  124. Raychaudhuri, A. (1994). Further results on t-coloring and frequency assignment problems. SIAM Journal on Discrete Mathematics, 7(4), 605–613. CrossRefGoogle Scholar
  125. Riihijärvi, J., Petrova, M., & Mähönen, P. (2005). Frequency allocation for WLANs using graph colouring techniques. In Proceedings of WONS’05, St. Moritz, Switzerland. Google Scholar
  126. ROADEF website. (2001). ROADEF Challenge. URL http://www.prism.uvsq.fr/~vdc/ROADEF/CHALLENGES/2001/challenge(2001)html.
  127. Roberts, F. S. (1991). t-colorings of graphs: Recent results and open problems. Discrete Mathematics, 93, 229–245. CrossRefGoogle Scholar
  128. Rouskas, A. N., Kazantzakis, M. G., & Anagnostou, M. E. (1995). Optimal channel assignment in cellular networks. International Journal of Communication Systems, 8, 359–364. Google Scholar
  129. Rushforth, C. K., & Wang, W. (1997). Local search for channel assignment in cellular mobile networks. In DIMACS series in discrete mathematics and theoretical computer science (Vol. 35, pp. 689–709). Providence: American Mathematical Society. Google Scholar
  130. Sandalidis, H. G., Stavroulakis, P. P., & Rodriguez-Tellez, J. (1999). Borrowing channel assignment strategies based on heuristic techniques for cellular systems. IEEE Transactions on Neural Networks, 10, 176–181. CrossRefGoogle Scholar
  131. Schiex, T., de Givry, S., & Sanchez, M. (2006). Toulbar2—an open source weighted constraint satisfaction solver. URL http://mulcyber.toulouse.inra.fr/projects/toulbar2/.
  132. Sivarajan, K. N., McEliece, R. J., & Ketchum, J. W. (1989). Channel assignment in cellular radio. In Proceedings of the 39th IEEE vehicular technology conference (pp. 846–850). Google Scholar
  133. Smith, D. H., Hurley, S., & Thiel, S. U. (1998). Improving heuristics for the frequency assignment problem. European Journal of Operational Research, 107, 76–86. CrossRefGoogle Scholar
  134. Smith, D. H., Taplin, R. K., & Hurley, S. (2001). Frequency assignment with complex co-site constraints. IEEE Transaction on Electromagnetic Compatibility, 43(2), 210–218. CrossRefGoogle Scholar
  135. Smith, D. H., Allen, S. M., & Hurley, S. (2002). Characteristics of good meta-heuristic algorithms for the frequency assignment problem. Annals of Operations Research, 107(1–4), 285–301. Google Scholar
  136. Smith, D. H., Hughes, L. A., Moon, J. N. J., & Montemanni, R. (2007). Measuring the effectiveness of frequency assignment algorithms. IEEE Transactions on Vehicular Technology, 56, 331–341. CrossRefGoogle Scholar
  137. Smith, K. A., & Palaniswami, M. (1997). Static and dynamic channel assignment using neural networks. IEEE Journal on Selected Areas in Communications, 15, 238–249. CrossRefGoogle Scholar
  138. Sung, C. W., & Wong, W. S. (1997). Sequential packing algorithm for channel assignment under cochannel and adjacent channel interference constraint. IEEE Transactions on Vehicular Technology, 46, 676–685. CrossRefGoogle Scholar
  139. Tcha, D., Chung, Y., & Choi, T. (1997). A new lower bound for the frequency assignment problem. IEEE/ACM Transactions on Networking, 5, 34–39. CrossRefGoogle Scholar
  140. Thuve, H. (1981). Frequency planning as a set partitioning problem. European Journal of Operational Research, 6, 29–37. CrossRefGoogle Scholar
  141. Tiourine, S. R., Hurkens, C. A. J., & Lenstra, J. K. (1995). An overview of algorithmic approaches to frequency assignment problems. In Calma symposium on combinatorial algorithms for military applications (pp. 53–62). Google Scholar
  142. Tsang, E., & Voudouris, C. (1998). Solving the radio link frequency assignment problem using guided local search. In NATO symposium on radio length frequency assignment, Aalborg, Denmark, 1998. http://cswww.essex.ac.uk/CSP/papers.html.
  143. Valenzuela, C., Hurley, S., & Smith, D. H. (1998). A permutation based genetic algorithm for minimum span frequency assignment. In Lecture notes in computer science (Vol. 1498, pp. 907–916). Google Scholar
  144. van Benthem, H. P. (1995). GRAPH generating radio link frequency assignment problems heuristically. Master’s thesis, Delft University of Technology. Google Scholar
  145. Verfaillie, G., Lemaître, M., & Schiex, T. (1996). Russian doll search for solving constraint optimization problems. In Proceedings of the 13th international conference on artificial intelligence (AAAI-96) (pp. 181–187), Portland, OR, USA. Google Scholar
  146. Villegas, E. G., Ferré, R. V., & Aspas, J. P. (2005). Implementation of a distributed dynamic channel assignment mechanism for IEEE 802.11 networks. In Proceedings of PIMRC 2005, September 2005. Google Scholar
  147. Vizing, V. G. (1965). Critical graphs with given chromatic class. Diskretniyi Analiz, 5, 9–17 (in Russian). Google Scholar
  148. Walser, J. P. (1996). Feasible cellular frequency assignment using constraint programming abstractions. In Proceedings of the workshop on constraint programming applications (CP96), Cambridge, MA, USA. Google Scholar
  149. Wang, L., & Gu, W. (2004). Genetic algorithms with stochastic ranking for optimal channel assignment in mobile communications. In Lecture notes in computer science (Vol. 3314, pp. 154–159). Google Scholar
  150. Wang, W., & Rushforth, C. K. (1996). An adaptive local-search algorithm for the channel-assignment problem (CAP). IEEE Transactions on Vehicular Technology, 45, 459–466. CrossRefGoogle Scholar
  151. Warners, J. P., Terlaky, T., Roos, C., & Jansen, B. (1997). A potential reduction approach to the frequency assignment problem. Discrete Applied Mathematics, 78, 251–282. CrossRefGoogle Scholar
  152. Yuan, D., Björklund, P., & Värbrand, P. (2002). Optimal frequency planning in mobile networks with frequency hopping. Technical Report LiTH-ITN-R-2002–3 Linköping University, Norrköping, Sweden submitted to Computers and Operations Research. Google Scholar
  153. Zerovnik, J. (1997). Experiments with a randomized algorithm for a frequency assignment problem. Technical Report 97–27, Ecole Normale Supérieure de Lyon. Google Scholar
  154. Zhang, M., & Yum, T. P. (1991). The nonuniform compact pattern allocation algorithm for cellular mobile systems. IEEE Transactions on Vehicular Technology, 40, 387–391. CrossRefGoogle Scholar
  155. Zoellner, J. A., & Beall, C. L. (1977). A breakthrough in spectrum conserving frequency assignment technology. IEEE Transactions on Electromagnetic Compatibility, 19, 313–319. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Karen I. Aardal
    • 1
  • Stan P. M. van Hoesel
    • 2
  • Arie M. C. A. Koster
    • 3
  • Carlo Mannino
    • 4
  • Antonio Sassano
    • 4
  1. 1.Centrum voor Wiskunde en Informatica (CWI)AmsterdamThe Netherlands
  2. 2.Department of Quantitative EconomicsUniversiteit MaastrichtMaastrichtThe Netherlands
  3. 3.Centre for Discrete Mathematics and its Applications (DIMAP)University of WarwickCoventryUK
  4. 4.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomaItaly

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