Approximation Results for Wavelength Routing in Directed Trees

The paper deals with wavelength routing in WDM (wavelength division multiplexing) optical networks. Wavelengths must be assigned to connection requests which are represented as directed paths, and it is required that paths receive different wavelengths if they share a directed link. The goal is to minimize the number of wavelengths used. Mihail et al. [10] conjectured that there is a solution for directed trees with at most b 2Lmaxc wavelengths where Lmax is the maximum load on a directed link. In this paper, we show that there exists a binary tree with load Lmax = 3 such that every solution needs at least 5 wavelengths. Furthermore, we present an approximation algorithm for binary trees with approximation ratio b 3Lmaxc b 3OPT c. This improves the bound b 7 4Lmaxc for binary trees given by Mihail et al. [10]. Finally, we show that no local greedy algorithm for binary trees can go below b 3Lmaxc. This ratio is the best ratio that can be achieved by any local greedy algorithm for this problem.

[1]  Vijay Kumar,et al.  Improved access to optical bandwidth in trees , 1997, SODA '97.

[2]  Klaus Jansen,et al.  Call scheduling in trees, rings and meshes , 1997, Proceedings of the Thirtieth Hawaii International Conference on System Sciences.

[3]  Satish Rao,et al.  Efficient access to optical bandwidth wavelength routing on directed fiber trees, rings, and trees of rings , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[4]  Klaus Jansen,et al.  Constrained Bipartite Edge Coloring with Applications to Wavelength Routing , 1997, ICALP.

[5]  Christos Kaklamanis,et al.  Efficient Wavelength Routing on Directed Fiber Trees , 1996, ESA.

[6]  Satish Rao,et al.  Efficient access to optical bandwidth , 1995, FOCS 1995.

[7]  Alastair D. McAulay,et al.  Optical computer architectures , 1991 .

[8]  Eli Upfal,et al.  Efficient routing in all-optical networks , 1994, STOC '94.

[9]  Klaus Jansen,et al.  An optimal greedy algorithm for wavelength allocation in directed tree networks , 1997, Network Design: Connectivity and Facilities Location.