Skip to main content

On the Complexity of Approximation and Online Scheduling Problems with Applications to Optical Networks

  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9224))

Included in the following conference series:

  • 599 Accesses

Abstract

We present scheduling problems that stem from optical networks, and discuss their complexity. We present lower bounds and inapproximability results for several optimization problems. They include offline and online scenarios, and concern problems that optimize the use of components in the optical networks, specifically Add-Drop Multiplexers (ADMs) and regenerators.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Akiyama, J., Chvátal, V.: A short proof of the linear arboricity for cubic graphs. Bull. Liberal Arts Sci. Nippon Med. Sch. 2, 1–3 (1981)

    Google Scholar 

  2. Alimonti, P., Kann, V.: Some APX-completeness results for cubic graphs. Theoret. Comput. Sci. 237(1–2), 123–134 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bermond, J.-C., Fouquet, J.L., Habib, M., Péroche, B.: On linear \(k\)-arboricity. Discrete Math. 52, 123–132 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  4. Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  5. Chen, S., Ljubic, I., Raghavan, S.: The regenerator location problem. Networks, 55(3), 205–220 (2010)

    MathSciNet  MATH  Google Scholar 

  6. Călinescu, G., Frieder, O., Wan, P.-J.: Minimizing electronic line terminals for automatic ring protection in general wdm optical networks. IEEE J. Sel. Area Commun. 20(1), 183–189 (2002)

    Article  Google Scholar 

  7. Călinescu, G., Wan, P.-J.: Traffic partition in wdm/sonet rings to minimize sonet ADMs. J. Comb. Optim. 6(4), 425–453 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Eilam, T., Moran, S., Zaks, S.: Lightpath arrangement in survivable rings to minimize the switching cost. IEEE J. Sel. Area Commun. 20(1), 172–182 (2002)

    Article  MathSciNet  Google Scholar 

  9. Epstein, L., Levin, A.: Better bounds for minimizing SONET ADMs. In: 2nd Workshop on Approximation and Online Algorithms, Bergen, Norway, September 2004

    Google Scholar 

  10. Fedrizzi, R., Galimberti, G.M., Gerstel, O., Martinelli, G., Salvadori, E., Saradhi, C.V., Tanzi, A., Zanardi, A.: Traffic independent heuristics for regenerator site selection for providing any-to-any optical connectivity. In: Proceedings of IEEE/OSA Conference on Optical Fiber Communications (OFC) (2010)

    Google Scholar 

  11. Flammini, M., Marchetti-Spaccamela, A., Monaco, G., Moscardelli, L., Zaks, S.: On the complexity of the regenerator placement problem in optical networks. IEEE/ACM Trans. Networking 19(2), 498–511 (2011)

    Article  Google Scholar 

  12. Flammini, M., Monaco, G., Moscardelli, L., Shachnai, H., Shalom, M., Tamir, T., Zaks, S.: Minimizing total busy time in parallel scheduling with application to optical networks. Theor. Comput. Sci. 411(40–42), 3553–3562 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Flammini, M., Shalom, M., Zaks, S.: On minimizing the number of ADMs in a general topology optical network. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 459–473. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Gerstel, O., Lin, P., Sasaki, G.: Wavelength assignment in a WDM ring to minimize cost of embedded SONET rings. In: INFOCOM 1998, Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies (1998)

    Google Scholar 

  15. Kim, S.W., Seo, S.W.: Regenerator placement algorithms for connection establishment in all-optical networks. IEEE Proc. Commun. 148(1), 25–30 (2001)

    Article  Google Scholar 

  16. Leonardi, S., Vitaletti, A.: Randomized lower bounds for online path coloring. In: Rolim, J.D.P., Serna, M., Luby, M. (eds.) RANDOM 1998. LNCS, vol. 1518, pp. 232–247. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  17. Mertzios, G.B., Sau, I., Shalom, M., Zaks, S.: Placing regenerators in optical networks to satisfy multiple sets of requests. IEEE Trans. Networking 20(6), 1870–1879 (2012)

    Article  MATH  Google Scholar 

  18. Mertzios, G.B., Shalom, M., Wong, P.W.H., Zaks, S.: Online regenerator placement. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 4–17. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  19. Pachnicke, S., Paschenda, T., Krummrich, P.M.: Physical impairment based regenerator placement and routing in translucent optical networks. In: Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, p. OWA2. Optical Society of America (2008)

    Google Scholar 

  20. Shalom, M., Wong, P.W., Zaks, S.: Optimal on-line colorings for minimizing the number of adms in optical networks. J. Discrete Algorithms 8(2), 174–188 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Shalom, M., Zaks, S.: A 10/7 + \(\epsilon \) approximation scheme for minimizing the number of ADMs in SONET rings. In: First Annual International Conference on Broadband Networks, San-José, California, USA, pp. 254–262, October 2004

    Google Scholar 

  22. Sriram, K., Griffith, D., Su, R., Golmie, N.: Static vs. Dynamic Regenerator Assignment in Optical Switches: models and Cost Trade-offs. Workshop on High Performance Switching and Routing (HPSR), pp. 151–155 (2004)

    Google Scholar 

  23. Thomassen, C.: Two-coloring the edges of a cubic graph such that each monochromatic component is a path of length at most 5. J. Comb. Theor. Ser. B 75(1), 100–109 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Yang, X., Ramamurthy, B.: Dynamic routing in translucent WDM optical networks. In: Proceedings of the IEEE International Conference on Communications (ICC), pp. 955–971 (2002)

    Google Scholar 

  25. Yang, X., Ramamurthy, B.: Sparse regeneration in translucent wavelength-routed optical networks: Architecture, network design and wavelength routing. Photonic Netw. Commun. 10(1), 39–53 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shmuel Zaks .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zaks, S. (2016). On the Complexity of Approximation and Online Scheduling Problems with Applications to Optical Networks. In: Mayr, E. (eds) Graph-Theoretic Concepts in Computer Science. WG 2015. Lecture Notes in Computer Science(), vol 9224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53174-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53174-7_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53173-0

  • Online ISBN: 978-3-662-53174-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics