Abstract
In this paper, we provide a polynomial-time approximation algorithm for Call Control and Routing problems in SONET rings. In this problem, we are given a SONET ring and a set of calls, each of which is described by a source-destination pair of nodes together with an integer specifying the call demand, the aim is to devise a routing scheme such that the total demand transmitted is maximum subject to the bandwidth restriction. We first give an \(\cal NP\)-hardness proof for this problem. Then a polynomial-time approximation algorithm is provided. When \(d_{max}\leq \frac{1}{K}d^* \) (where K > 2 is a constant, d * is the available bandwidth of the ring and d max is the largest call demand among all the calls), the algorithm outputs a routing scheme with total demand transmitted at least as \((1-\frac{7}{2K+3})\) times the optimum.
Research is supported by NCET(No. 05-098), NSFC(No. 10371114).
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References
Adamy, U., Abbuehl, C., Anand, R.S., Erlebach, T.: Call control in rings. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 788–799. Springer, Heidelberg (2002)
Chekuriy, C., Mydlarzz, M., Shepherd, F.B.: Multicommodity demand flow in a tree. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 410–425. Springer, Heidelberg (2003)
Cosares, S., Saniee, I.: An optimization problem related to balancing loads on SONET rings. Telecommunications Systems 3, 165–181 (1992)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A guide to the Theory of \(\cal NP\)-Completeness. W.H. Freeman, San Fransisco (1979)
Khanna, S.: A polynomial-time approximation scheme for the SONET ring loading problem. Bell Labs Technical Journal 2(2) (1997)
Ramaswami, R., Sivarajan, K.N.: Optical Networks: A Practical Perspective, 2nd edn. Morgan Kaufmann Publishers, San Francisco (2002)
Anand, R.S., Erlebach, T.: Routing anc call control algorithms for ring networks. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 186–197. Springer, Heidelberg (2003)
Schrijver, A., Seymour, P., Winkler, P.: The ring loading problem. SIAM Journal on Discrete Mathematics 11, 1–14 (1998)
Wilfong, P., Winkler, P.: Ring routing and wavelength translation. In: SODA. Proceedings of Ninth Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 333–341. ACM Press, New York (1998)
Wan, P., Yang, Y.: Load-balanced routing in counter rotated SONET rings. Networks 35, 279–286 (2000)
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Chen, S., Fang, Q. (2007). Call Control and Routing in SONET Rings. In: Chen, B., Paterson, M., Zhang, G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. ESCAPE 2007. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74450-4_24
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DOI: https://doi.org/10.1007/978-3-540-74450-4_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74449-8
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