Abstract
We present randomized approximation algorithms for the circular arc graph colouring problem and for the problem of bandwidth allocation in all-optical ring networks. We obtain a factor-of-(1+1/e+o(1)) randomized approximation algorithm for the arc colouring problem, an improvement over the best previously known performance ratio of 5/3. For the problem of allocating bandwidth in an all-optical WDM (wavelength division multiplexing) ring network, we present a factor-of-(1.5+1/2e+o(1)) randomized approximation algorithm, improving upon the best previously known performance ratio of 2.
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References
Azuma, K. Weighted Sum of Certain Dependent Random Variables. Tohoku Mathematical Journal, 19:357–367, 1967.
Cosares, S., Carpenter, T., and Saniee, I. Static Routing and Slotting of Demand in SONET Rings. Presented at the TIMS/ORSA Joint National Meeting, Boston, MA, 1994.
Erlebach, T. and Jansen, K. Call Scheduling in Trees, Rings and Meshes. In Proc. 30th Hawaii International Conf. on System Sciences, 1997.
Even, S., Itai, A., and Shamir, A. On the complexity of timetable and multicommodity flow problems, SIAM Journal of Computing, 5(1976),691–703.
Garey, M.R., Johnson, D.S., Miller, G.L. and Papadimitriou, C.H. The Complexity of Coloring Circular Arcs and Chords. SIAM J. Alg. Disc. Meth., 1(2):216–227, 1980.
Golumbic, M. C, Algorithmic Graph Theory and Perfect Graphs, Academic Press, 1980.
Kaklamanis, C. and Persiano, P. Efficient wavelength routing on directed fiber trees. In Proc. 4th Annual European Symposium on Algorithms, 1996.
Kumar, V. and Schwabe, E.J. Improved access to optical bandwidth in trees. In Proc 8th Annual ACM-SIAM Symp. on Discrete Algorithms, pp. 437–444, 1997.
McDiarmid, C. On the method of bounded differences. In J. Siemons, editor, Surveys in Combinatorics, volume 141 of LMS Lecture Notes Series, pages 148–188. 1989.
Mihail, M., Kaklamanis, C, and Rao, S. Efficient Access to Optical Bandwidth. In Proc IEEE Symp on Foundations of Comp Sci, pp. 548–557, 1995.
Motwani, R., and Raghavan, P. Randomized Algorithms, Cambridge University Press, 1995.
Orlin, J.B., Bonuccelli, M.A., and Bovet, D.P. An O(n 2) Algorithm for Coloring Proper Circular Arc Graphs. SIAM J. Alg. Disc. Meth., 2(2):88–93, 1981.
Raghavan, P. Randomized Rounding and Discrete Ham-Sandwiches: Provably Good Algorithms for Routing and Packing Problems. PhD Thesis, CS Division, UC Berkeley, 1986.
Raghavan, P., and Upfal, E. Efficient Routing in All-Optical Networks. In Proc 26th ACM Symp on Theory of Computing, pp. 134–143, 1994.
Shih, W.K. and Hsu, W.L. An Approximation Algorithm for Coloring Circular-Arc Graphs. SIAM Conference on Discrete Mathematics, 1990.
Settembre, M. and Matera, F. All-optical implementations of high capacity TDMA networks. Fiber and Integrated Optics, 12:173–186, 1993.
Tucker, A. Coloring a Family of Circular Arcs. SIAM J. Appl. Math., 29(3):493–502, 1975.
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© 1998 Springer-Verlag Berlin Heidelberg
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Kumar, V. (1998). Approximating circular arc colouring and bandwidth allocation in all-optical ring networks. In: Jansen, K., Rolim, J. (eds) Approximation Algorithms for Combinatiorial Optimization. APPROX 1998. Lecture Notes in Computer Science, vol 1444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053971
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DOI: https://doi.org/10.1007/BFb0053971
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