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Fractional and Integral Coloring of Locally-Symmetric Sets of Paths on Binary Trees

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Approximation and Online Algorithms (WAOA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2909))

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Abstract

Motivated by the problem of allocating optical bandwidth in tree–shaped WDM networks, we study the fractional path coloring problem in trees. We consider the class of locally-symmetric sets of paths on binary trees and prove that any such set of paths has a fractional coloring of cost at most 1.367L, where L denotes the load of the set of paths. Using this result, we obtain a randomized algorithm that colors any locally-symmetric set of paths of load L on a binary tree (with reasonable restrictions on its depth) using at most 1.367L+o(L) colors, with high probability.

This work was partially funded by the European Union under IST FET Project ALCOM–FT, IST FET Project CRESCCO and RTN Project ARACNE.

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References

  1. Auletta, V., Caragiannis, I., Kaklamanis, C., Persiano, P.: Randomized Path Coloring on Binary Trees. Theoretical Computer Science 289(1), 355–399 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Caragiannis, I., Ferreira, A., Kaklamanis, C., Perennes, S., Rivano, H.: Fractional Path Coloring with Applications to WDM Networks. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 732–743. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Caragiannis, I., Kaklamanis, C., Persiano, P.: Symmetric Communication in All– Optical Tree Networks. Parallel Processing Letters 10(4), 305–313 (2000)

    Article  Google Scholar 

  4. Corteel, S., Gardy, D., Barth, D., Denise, A., Valencia-Pabon, M.: On the Complexity of Routing Permutations on Trees by Arc-Disjoint Paths. In: Gonnet, G.H., Viola, A. (eds.) LATIN 2000. LNCS, vol. 1776, pp. 308–317. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Erlebach, T., Jansen, K.: The Complexity of Path Coloring and Call Scheduling. Theoretical Computer Science 255(1-2), 33–50 (2000)

    Article  MathSciNet  Google Scholar 

  6. Erlebach, T., Jansen, K., Kaklamanis, C., Mihail, M., Persiano, P.: Optimal Wavelength Routing in Directed Fiber Trees. Theoretical Computer Science 221(1-2), 119–137 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kumar, V.: Approximating Circular Arc Colouring and Bandwidth Allocation in All–Optical Ring Networks. In: Jansen, K., Rolim, J.D.P. (eds.) APPROX 1998. LNCS, vol. 1444, pp. 147–158. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  8. Kumar, V., Schwabe, E.: Improved Access to Optical Bandwidth in Trees. In: Proc. of the 8th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA 1997), pp. 437–444 (1997)

    Google Scholar 

  9. Raghavan, P., Upfal, E.: Efficient Routing in All-Optical Networks. In: Proc. of the 26th Annual Symposium on Theory of Computing (STOC 1994), pp. 133–143 (1994)

    Google Scholar 

  10. Ramaswami, R., Sivarajan, K.: Optical Networks: A Practical Perspective. Morgan Kauffman Publishers, San Francisco (1998)

    Google Scholar 

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Caragiannis, I., Kaklamanis, C., Persiano, P., Sidiropoulos, A. (2004). Fractional and Integral Coloring of Locally-Symmetric Sets of Paths on Binary Trees. In: Solis-Oba, R., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2003. Lecture Notes in Computer Science, vol 2909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24592-6_7

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  • DOI: https://doi.org/10.1007/978-3-540-24592-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21079-5

  • Online ISBN: 978-3-540-24592-6

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