Coloring all directed paths in a symmetric tree, with an application to optical networks

Journal of Graph Theory

Volumn 38, Issue 4, 2001, Pages 183-196

  Gargano, Luisa ^a,d   Hell, Pavol ^a,b   Perennes, Stephane ^a,c  

^a UNIVERSITY OF SALERNO   (Italy)

^b SIMON FRASER UNIVERSITY   (Canada)

^c INRIA   (France)

^d Dipartimento di Informatica ed Applicazioni   (Italy)

Author keywords

Colors; Optical networks; Symmetric directed tree

Indexed keywords

EID: 31244436619     PISSN: 03649024     EISSN: None     Source Type: Journal    
DOI: 10.1002/jgt.10002     Document Type: Article

References (25)

1. A. Aggarwal, A. Bar-Noy, D. Coppersmith, R. Ramaswami, B. Schieber, and M. Sudan, "Efficient routing and scheduling algorithms for optical networks," Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'94), 1994, pp. 412-423.
2. Y. Aumann and Y. Rabani, "Improved bounds for all optical routing," Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'95), 1995, pp. 567-576.
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," Proceedings of 2nd Workshop on Optics and Computer Science (WOCS), Geneve, Switzerland, April 1997.
4. J.-C. Bermond, L. Gargano, S. Perennes, A. Rescigno, and U. Vaccaro, "Efficient collective communications in optical networks" in Theoretical Computer Science, 233 ,1-2 (2000), 165-189.
5. J. A. Bondy and U. S. R. Murty, Graph Theory and Applications, Elsevier, New York, 1976.
6. N. K. Cheung, K. Nosu, and G. Winzer. IEEE JSAC: (Special Issue on Dense WDM Networks) 8 (1990).
7. T. Erlebach and K. Jansen, "Scheduling of virtual connections in fast networks," Proc of 4th Workshop on Parallel Systems and Algorithms PASA 1996, 1996, pp. 13-32.
8. L. R. Ford and D. R. Fulkerson, Flows in Networks, Princeton University Press, Cambridge, MA, 1962.
9. L. Gargano, "Limited wavelength conversion in all-optical tree networks," Proceedings of 25th International Colloquium on Automata, Languages, and Programming (ICALP 98), Aalborg, July 1998.
10. L. Gargano, P. Hell, and S. Perennes, "Colouring directed paths in symmetric trees, with an application to optical networks," Proceedings of 24th International Colloquium on Automata, Languages, and Programming (ICALP 97), P. Degano, R. Gorrieri, A. Marchetti-Spaccamela (editors), LNCS 1256, Springer, Bologna, 1997.
11. M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
12. M. C. Golumbic and R. E. Jamison, The edge intersection graphs of paths in a tree J. Combin Theory B 38 (1985), 8-22.
13. P. E. Green. 'The future of fiber-optic computer networks,' IEEE Comp, 24 (1991), 78-87.
14. P. E. Green, Fiber-Optic Communication Networks, Prentice-Hall, 1992.
15. K. Jansen, Approximation results for wavelength routing in directed trees, in preparation.
16. C. Kaklamanis and P. Persiano, Efficient Wavelength Routing on Directed Fiber Trees, ESA' 96, Barcelona Springer, LNCS 11, pp. 460-470.
17. L. Lovasz, A characterization of perfect graphs, J Comb Theory B 13 (1972), 95-98.
18. A. D. McAulay, Optical Computer Architectures, Wiley, New York, 1991.
19. M. Mihail, C. Kaklamanis, and S. Rao, "Efficient access to optical bandwidth," Proceedings of 36th Annual IEEE Symposium on Foundations of Computer Science (FOCS'95), 1995, pp. 548-557.
20. C. L. Monma and V. K. Wei, Intersection graphs of paths in a tree, J Comb Theory B 41 (1986), 141-181.
21. R. Ramaswami, Multi-wavelength lightwave networks for computer communication, IEEE Communi Magazine 31 (1993), 78-88.
22. P. Raghavan and E. Upfal. "Efficient routing in all-optical Networks," Proceedings of the 26th Annual ACM Symposium on Theory of Computing (STOC'94), 1994, pp. 134-143.
23. H. J. Ryser, Combinatorial Mathematics, The Carus Mathematical Monographs (number 14), The Mathematical Association of America, 1973.
24. R. J. Vetter and D. H. C. Du, Distributed computing with high-speed optical networks, IEEE Comput 26 (1993), 8-18.
25. G. Wilfong and P. Winkler, "Ring routing and wavelength Translation," Proceedings of 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'98).