Tight LP-based lower bounds for wavelength conversion in optical networks

Statistica Neerlandica

Volumn 61, Issue 1, 2007, Pages 115-136

  Koster, Arie M C A ^a   Zymolka, Adrian ^b  

^a ZUSE INSTITUTE BERLIN   (Germany)

^b ATESIO GMBH   (Germany)

Author keywords

Column generation; Integer programming; Wavelength assignment

Indexed keywords

EID: 33846881305     PISSN: 00390402     EISSN: 14679574     Source Type: Journal    
DOI: 10.1111/j.1467-9574.2007.00351.x     Document Type: Article

References (27)

1. AARDAL, K. I., C. P. M. VAN HOESEL, A. M. C. A. KOSTER, C. MANNING and A. SASSANO (2003), Models and solution techniques for the frequency assignment problem 4OR, 1, 261-317.
2. ANDREWS, M. and L. ZHANG (2006), Complexity of wavelength assignment in optical network optimization, in Proceedings of IEEE INFOCOM. Barcelona, Spain.
3. BETKER, A., C. GERLACH, R. HÜLSERMANN, M. JÄGER, M. BARRY, S. BODAMER, J. SPÄTH, C. GAUGER and M. KÖHN (2003), Reference transport network scenarios. Technical report, BMBF MultiTeraNet. http://www.ikr.uni-stuttgart.de/IKRSimLib/Referenz_Netze_v14_full.pdf.
4. CARAGIANNIS, I., C. KAKLAMANIS and P. PERSIANO (2001), Wavelength routing in all-optical tree networks: a survey, Computers and Informatics 20, 95-120.
5. CHVÁTAL, V. (1983), Linear Programming, W.H. Freeman and Company, New York.
6. DESROSIERS, J. and M. E. LÜBBECKE, (2005), A primer in column generation, in: G. DESAULNIERS, J. DESROSIERS and M. M. SOLOMON (eds.), Column Generation, Kluwer Academic Publishers, Boston, MA.
7. DUTTA, R. and G. ROUSKAS (2000), A survey of virtual topology design algorithms for wavelength routed optical networks, Optical Networks Magazine 1, 73-89.
8. DWIVEDI, A. and R. E. WAGNER (2000), Traffic model for USA long-distance optical network. In OFC 2000, pages 156-158. Optical Fiber Communications Conference, Volume 1, Baltimore, MD, USA
9. FERREIRA, A., S. PÉRENNES, A. W. RICHA, H. RIVANO and N. S. MOSES (2003), Models, complexity and algorithms for the design of multifiber WDM networks, Telecommunication Systems 24, 123-138.
10. ILOG (2003), CPLEX, version 9.0, http://www.ilog.com/ products/cplex.
11. JAUMARD, B., C. MEYER and B. THIONGANE (2006), ILP formulations for the RWA problem: symmetric systems, in: M. G. C. RESENDE and P. M. PARDALOS (eds.), Handbook of optimization in telecommunications, chapter 23, Springer Science+Business Media, New York, 637-677.
12. KLEINBERG, J. and A. KUMAR (2001), Wavelength conversion in optical networks, Journal of Algorithms 38, 25-50.
13. KOSTER, A. M. C. A. (2005), Wavelength assignment in multifiber WDM networks, in: Proceedings of INOC 2005, International Network Optimization Conference, Lisbon, Portugal, 60-66.
14. KOSTER, A. M. C. A. and A. ZYMOLKA (2004), Minimum converter wavelength assignment in all-optical networks, in: Proceedings of ONDM 2004, Ghent, Belgium, 517-535.
15. KOSTER, A. M. C. A. and A. ZYMOLKA (2005), Provably good solutions for wavelength assignment in optical networks, in Proceedings of ONDM 2005, Milan, Italy, 335-345.
16. KOSTER, A. M. C. A., A. ZYMOLKA, M. JÄGER and R. HÜLSERMANN (2005), Demand-wise shared protection for meshed optical networks, Journal of Network and Systems Management 13, 35-55.
17. LEE, T. L., K. LEE and S. PARK (2000), Optimal routing and wavelength assignment in WDM ring networks, IEEE Journal on Selected Areas in Communications 18, 2146-2154.
18. LI, G. and R. SIMHA (2001), On the wavelength assignment problem in multifiber WDM star and ring networks, IEEE ACM Transactions on Networking 9, 60-68.
19. LOVÁSZ, L. (1978), Kneser's conjecture, chromatic numbers and homotopy, Journal of Combinatorial Theory Series A 25, 319-324.
20. MEHROTRA, A. and M. A. TRICK (1996), A column generation approach for graph coloring, INFORMS Journal on Computing 8, 344-354.
21. NEMHAUSER, G. L. and L. A. WOLSEY (1988), Integer and Combinatorial Optimization, Wiley, New York.
22. PARDALOS, P., T. MAVRIDOU, and J., XUE (1998), The graph coloring problem: a bibliographic survey, in: D.-Z. DU and P. PARDALOS (eds.), Handbook of combinatorial optimization, volume 2, Kluwer Academic Publishers, Hingham, MA, USA, 331-395.
23. VIZING, V. G. (1964), On an estimate of the chromatic class of a p-graph (in Russian), Diskretnyǐ Analiz. 3, 25-30.
24. WINKLER, P. and L. ZHANG (2003), Wavelength assignment and generalized interval graph coloring, in: Proc. 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 830-831. Baltimore, MD, USA.
25. ZANG, H., J. JUE and B. MUKHERJEE (2000), A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks. Optical Networks Magazine 1, 47-60.
26. ZYMOLKA, A. (2006), Design of survivable optical networks by mathematical optimization, PhD thesis, Technical University Berlin.
27. ZYMOLKA, A., A. M. C. A. KOSTER and R. WESSÄLY (2003), Transparent optical network design with sparse wavelength conversion, in: Proceedings of ONDM 2003, Budapest, Hungary, 61-80.