Optical Routing of Uniform Instances in Tori
We consider the problem of routing uniform communication instances in switched optical tori that use the wavelength division multplexing (or WDM) approach. A communication instance is called uniform if it consists exactly of all pairs of nodes in the graph whose distance is equal to one from a specified set S = d 1; d2;...; d k. We give bounds on the optimal load induced on an edge for any uniform instance in a torus Tnxn. When k = 1, we prove necessary and sufficient conditions on the value in S relative to n for the wavelength index to be equal to the load. When k≥ 2, we show that for any set S, there exists an n0, such that for all n > n0, there is an optimal wavelength assignment for the communication instance specified by S on the torus Tnxn. We also show an approximation for the wavelength index for any S and n. Finally, we give some results for rectangular tori.
KeywordsOptical Network Vertical Edge Horizontal Edge Wavelength Assignment Communication Instance
Unable to display preview. Download preview PDF.
- 2.B. Beauquier. All-to-all communication for some wavelength-routed all-optical networks. Technical report, INRIA Sophia-Antipolis, 1998.Google Scholar
- 3.B. Beauquier, J.-C. Bermond, L. Gargano, P. Hell, S. Perennes, and U. Vaccaro. Graph problems arising from wavelength-routing in all-optical networks. In Proceedings of the 2nd Workshop on Optics and Computer Science (WOCS), part of IPPS, April 1997.Google Scholar
- 5.N.K. Cheung, K. Nosu, and G. Winzer. An introduction to the special issue on dense WDM networks. IEEE J. Selected Areas in Communications, 8:945–947, 1990.Google Scholar
- 6.T. Erlach and K. Jansen. Scheduling of virtual connections in fast networks. In Proceedings of the 4-th Workshop on Parallel Systems and Algorithms, pages 13–32, 1996.Google Scholar
- 7.M. Mihail, C. Kaklamanis, and S. Rao. Efficient access to optical bandwidth. In FOCS, pages 548–557, 1995.Google Scholar
- 8.L. Narayanan and J. Opatrny. Wavelength routing of uniform instances in optical rings. In Proceedings of ARACNE 2000, 2000. To appear.Google Scholar
- 9.L. Narayanan, J. Opatrny, and D. Sotteau. All-to-all optical routing in chordal rings of degree four. In Proceedings of the Symposium on Discrete Algorithms, pages 695–703, 1999.Google Scholar
- 10.J. Opatrny. Uniform multi-hop all-to-all optical routings in rings. In Proceedings of LATIN’2000, LNCS 1776, pages 237–246, 2000.Google Scholar
- 11.H. Schroder, O. Sykora, and I. Vrto. Optical all-to-all communication for some product graphs. In Theory and Practice of Informatics, Seminar on Current Trends in Theory and Practice of Informatics, LNCS, volume 24, 1997.Google Scholar