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Decidable Properties of Graphs of All-Optical Networks

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Automata, Languages and Programming (ICALP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

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Abstract

We examine several decidability questions suggested by questions about all-optical networks, related to the gap between maximal load and number of colors (wavelengths) needed for a legal routing on a fixed graph. We prove the multiple fiber conjecture: for every fixed graph G there is a number L G such that in the communication network with L G parallel fibers for each edge of G, there is no gap (for any load). We prove that for a fixed graph G the existence of a gap is computable, and give an algorithm to compute it. We develop a decomposition theory for paths, defining the notion of prime sets of paths that are finite building blocks for all loads on a fixed graph. Properties of such decompositions yield our theorems.

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References

  1. R. P. Anstee. An algorithmic proof of Tutte’s f-factor theorem. Journal of Algorithms, 6:112–131, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  2. B. Beauquier, J.-C. Bermond, L. Gargano, P. Hell, S. Perennes, and U. Vaccaro. Graph problems arising from wavelength-routing in all-optical networks. Proc. Of Workshop on Optics in Computer Science WOCS’97

    Google Scholar 

  3. N. K. Cheung, N. K., and G. Winzer. Special issue on dense WDM networks. Journal on Selected Areas in Communications, 8, 1990.

    Google Scholar 

  4. T. Erlebach and K. Jansen. Scheduling of virtual connections in fast networks. In Proc. of Parallel Systems and Algorithms (PASA), pages 13–32, 1996.

    Google Scholar 

  5. T. Erlebach and K. Jansen. Call scheduling in trees, rings and meshes. In Proc. of HICSS, 1997.

    Google Scholar 

  6. M. C. Golumbic and R. E. Jamison. The edge intersection graphs of paths in a tree. Journal of Combinatorial Theory, Series B, 38:8–22, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. E. Green. Fiber-optic communication networks. Prentice-Hall, 1993.

    Google Scholar 

  8. I. Holyer. The NP-completeness of edge coloring. SIAM Journal of Computing, 10(4):718–720, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  9. C. Kaklamanis, G. Persiano, T. Erlebach,and K. Jansen. Constrained bipartite edge coloring with applications to wavelength routing. Proc. of ICALP’97, Lecture notes in Computer Science vol. 1256:493–504, 1997.

    Google Scholar 

  10. R. Klasing. Methods and problems of wavelength-routing in all-optical networks. In Proc. of the MFCS’98 Workshop on Communication, 1998.

    Google Scholar 

  11. J. Kleinberg and A. Kumar. Wavelength conversion in optical networks In Proc. 10th ACM-SIAM Symposium on Discrete Algorithms, 1999.

    Google Scholar 

  12. G. Li and R. Simha On the wavelength assignment problem in multifiber WDM star and ring networks In Proc. IEEE INFOCOM, 2000.

    Google Scholar 

  13. L. Lovász. On chromatic number of finite set-systems. Acta Math. Acad. Sci. Hungar, 19:59–67, 1968.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. D. McAulay. Optical computer architectures. John Wiley, 1991.

    Google Scholar 

  15. L. Margara and J. Simon Wavelength assignment problem on all-optical networks with k fibers per link Proc. of ICALP2000, Lecture notes in Computer Science vol. 1853:768–779, 2000.

    Google Scholar 

  16. M. Mihail, C. Kaklamanis, and S. Rao. Efficient access to optical bandwidth— wavelength routing on directed fiber trees, rings, and trees of rings. In Proc. Of 36th IEEE-FOCS, pp. 548–557, 1995.

    Google Scholar 

  17. R. K. Pankaj and R. G. Gallager. Wavelength requirements of all-optical networks. IEEE/ACM Trans. on Networking, 3:269–280, 1995.

    Article  Google Scholar 

  18. J. Petersen. Die Theorie der Regulären Graphen. Acta Math. 15, 193–220, 1891.

    Article  MathSciNet  Google Scholar 

  19. R. Ramaswami. Multiwavelength lightwave networks for computer communication. IEEE Communications Magazine, 31(2):78–88, Feb. 1993.

    Article  Google Scholar 

  20. R. E. Tarjan. Decomposition by clique separators. Discrete Mathematics, 55(2):221–232, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  21. A. Tucker. Coloring a family of circular arcs. SIAM Journal of Applied Mathematics, 29(3):493–502, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  22. R. J. Vetter and D. H. C. Du. Distributed computing with high-speed optical networks. IEEE Computer, 26(2):8–18, Feb. 1993.

    Google Scholar 

  23. G. Wilfong and P. Winkler. Ring routing and wavelength translation. In Proc. Of the 9th Annual ACM-SIAM Symposium on on Discrete Algorithms (SODA), pp. 333–341, 1998.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Department, University of Bologna, Italy

    Luciano Margara

  2. Computer Science Department, University of Chicago, USA

    Janos Simon

Authors
  1. Luciano Margara
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  2. Janos Simon
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Margara, L., Simon, J. (2001). Decidable Properties of Graphs of All-Optical Networks. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_43

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  • DOI: https://doi.org/10.1007/3-540-48224-5_43

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

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