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On the complexity of the regenerator placement problem in optical networks

Published: 11 August 2009 Publication History

Abstract

Placement of regenerators in optical networks has attracted the attention of recent research works in optical networks. In this problem we are given a network, with an underlying topology of a graph G, and with a set of requests that correspond to paths in G. There is a need to put a regenerator every certain distance, because of a decrease in the power of the signal. In this work we investigate the problem of minimizing the number of locations to place the regenerators. We present analytical results regarding the complexity of this problem, in four cases, depending on whether or not there is a bound on the number of regenerators at each node, and depending on whether or not the routing is given or only the requests are given (and part of the solution is also to determine the actual routing). These results include polynomial time algorithms, NP-complete results, approximation algorithms, and inapproximability results.

References

[1]
G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela and M. Protasi. Complexity and Approximation, Combinatorial Optimization Problems and Their Approximability Properties. Springer-verlag, 1999.
[2]
C. A. Brackett, A. S. Acampora, J. Sweitzer, G. Tangonan, M. T. Smith, W. Lennon, K.-C. Wang, R.H. Hobbs. A scalable multiwavelength multihop optical network: a proposal forresearch on all-optical networks. Journal of Lightwave Technology, 11(5), pp. 736--753, 1993.
[3]
I. Caragiannis, C. Kaklamanis and P. Kanellopoulos. Energy-Efficient Wireless Network Design. Theory of Comput. Syst., 39(5), pp. 593--617, 2006.
[4]
S. Chen and S. Raghavan. The Regenerator Location Problem. In Proceedings of the International Network Optimization Conference (INOC 2007).
[5]
V. Chvatal. A greedy heuristic for the set-covering problem. Math. Oper. Res., 4(3), pp. 233--235, 1979.
[6]
T. Erlebach and S. Stefanakos. Wavelength Conversion in All-Optical Networks with Shortest-Path Routing. Algorithmica, 43(1--2), pp. 43--61, 2005.
[7]
U. Feige. A threshold of ln n for approximating set cover. Journal of the ACM, 45(4), pp. 634--652, 1998.
[8]
M. Garey and D. S. Johnson. Computers and Intractability, A Guide to the Theory of NP-Completeness. Freeman, 1979.
[9]
S. Guha and S. Khuller. Improved Methods for Approximating Node Weighted Steiner Trees and Connected Dominating Sets. Infomation and Computation, 150(1), pp. 57--74, 1999.
[10]
J. M. Kleinberg and A. Kumar. Wavelength Conversion in Optical Networks. Journal of Algorithms, 38(1), pp. 25--50, 2001.
[11]
S. W. Kim and S. W. Seo. Regenerator placement algorithms for connection establishment in all-optical networks. IEEE Proceedings Communications, 148(1), pp. 25--30, 2001.
[12]
S. Pachnicke, T. Paschenda and P. M. Krummrich. Physical Impairment Based Regenerator Placement and Routing in Translucent Optical Networks. Proceedings of the Optical Fiber communication/National Fiber Optic Engineers Conference,(OFC/NFOEC 2008), pp. 1--3, 2008.
[13]
B. Ramamurthy, H. Feng, D. Datta, J. P. Heritage and B. Mukherjee. Transparent vs. opaque vs. translucent wavelength-routed optical networks. Proceedings of the Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, (OFC/IOOC 99), pp. 59--61, 1999.
[14]
C. V. Saradhi and S. Zaks. Placement of regenerators in optical networks. In preparation.
[15]
K. Sriram, D. Griffith, R. Su and N. Golmie. Static vs. dynamic regenerator assignment in optical switches: models and cost trade-offs. Proceedings of the Workshop on High Performance Switching and Routing, (HPSR 2004), pp. 151--155, 2004.
[16]
G.T. Wilfong and P. Winkler. Ring Routing and Wavelength Translation. Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA 1998),pp. 333--341, 1998.
[17]
X. Yang and B. Ramamurthyn. Sparse Regeneration in Translucent Wavelength-Routed Optical Networks: Architecture, Network Design and Wavelength Routing. Photonic Network Communications, 10(1), pp. 39--53, 2005.
[18]
X. Yang and B. Ramamurthy. Dynamic routing in translucent WDM optical networks. Proceedings of the IEEE International Conference on Communications (ICC 2002),pp. 2796--2802, 2002.

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    cover image ACM Conferences
    SPAA '09: Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
    August 2009
    370 pages
    ISBN:9781605586069
    DOI:10.1145/1583991
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Published: 11 August 2009

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    Author Tags

    1. approximation algorithms
    2. complexity
    3. optical networks
    4. regenerators
    5. wavelength division multiplexing (wdm)

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    • (2014)Benders decomposition algorithms for the fixed-charge relay network design in telecommunicationsTelecommunications Systems10.1007/s11235-013-9763-556:4(441-453)Online publication date: 1-Aug-2014
    • (2012)Optimizing Busy Time on Parallel MachinesProceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium10.1109/IPDPS.2012.31(238-248)Online publication date: 21-May-2012
    • (2012)Cost efficient traffic grooming and regenerator placement in impairment-aware optical WDM networksOptical Switching and Networking10.1016/j.osn.2011.03.0109:3(225-239)Online publication date: Jul-2012
    • (2012)Online optimization of busy time on parallel machinesProceedings of the 9th Annual international conference on Theory and Applications of Models of Computation10.1007/978-3-642-29952-0_43(448-460)Online publication date: 16-May-2012
    • (2011)On the dimensioning of WDM optical networks with impairment-aware regenerationIEEE/ACM Transactions on Networking10.1109/TNET.2010.209054019:3(735-746)Online publication date: 1-Jun-2011
    • (2011)Biased random-key genetic algorithms with applications in telecommunicationsTOP10.1007/s11750-011-0176-x20:1(130-153)Online publication date: 23-Mar-2011
    • (2010)Placing regenerators in optical networks to satisfy multiple sets of requestsProceedings of the 37th international colloquium conference on Automata, languages and programming: Part II10.5555/1880999.1881036(333-344)Online publication date: 6-Jul-2010
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    • (2010)Impairment-aware path selection and regenerator placement in translucent optical networksProceedings of the The 18th IEEE International Conference on Network Protocols10.1109/ICNP.2010.5762750(11-20)Online publication date: 5-Oct-2010
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