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.
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References
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)
Alimonti, P., Kann, V.: Some APX-completeness results for cubic graphs. Theoret. Comput. Sci. 237(1–2), 123–134 (2000)
Bermond, J.-C., Fouquet, J.L., Habib, M., Péroche, B.: On linear \(k\)-arboricity. Discrete Math. 52, 123–132 (1984)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Chen, S., Ljubic, I., Raghavan, S.: The regenerator location problem. Networks, 55(3), 205–220 (2010)
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)
Călinescu, G., Wan, P.-J.: Traffic partition in wdm/sonet rings to minimize sonet ADMs. J. Comb. Optim. 6(4), 425–453 (2002)
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)
Epstein, L., Levin, A.: Better bounds for minimizing SONET ADMs. In: 2nd Workshop on Approximation and Online Algorithms, Bergen, Norway, September 2004
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)
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)
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)
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)
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)
Kim, S.W., Seo, S.W.: Regenerator placement algorithms for connection establishment in all-optical networks. IEEE Proc. Commun. 148(1), 25–30 (2001)
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)
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)
Mertzios, G.B., Shalom, M., Wong, P.W.H., Zaks, S.: Online regenerator placement. In: Fernà ndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 4–17. Springer, Heidelberg (2011)
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)
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)
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
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)
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)
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)
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)
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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
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DOI: https://doi.org/10.1007/978-3-662-53174-7_3
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