Improving the performance guarantee for approximate graph coloring
Journal of the ACM (JACM)
A still better performance guarantee for approximate graph coloring
Information Processing Letters
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Improved non-approximability results
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Optical networks: a practical perspective
Optical networks: a practical perspective
Efficient routing and scheduling algorithms for optical networks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Improved hardness results for approximating the chromatic number
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
On Wavelength Assignment in WDM Optical Networks
MPPOI '97 Proceedings of the 4th International Conference on Massively Parallel Processing Using Optical Interconnections
Routing and wavelength assignment in all-optical wdm wavelength-routing networks
Routing and wavelength assignment in all-optical wdm wavelength-routing networks
Graphs and Hypergraphs
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We address the issue of inapproximability of the wavelength assignment problem in wavelength division multiplexing (WDM) optical networks. We prove that in an n-node WDM optical network with m lightpaths and maximum load L, if NP ≠ ZPP, for any constant δ0, no polynomial time algorithm can achieve approximation ratio n1/2−δ or m1−δ, where NP is the class of problems which can be solved by nondeterministic polynomial time algorithms, and ZPP is the class of problems that can be solved by polynomial randomized algorithms with zero probability of error. Furthermore, the above result still holds even when L=2. We also prove that no algorithm can guarantee the number of wavelengths to be less than $$(\sqrt{n}/2)L$$ or (m/2)L. This is the first time inapproximability results are established for the wavelength assignment problem in WDM optical networks. We also notice the following fact, namely, there is a polynomial time algorithm for wavelength assignment which achieves approximation ratio of O(m(log log m)2/(log m)3). Therefore, the above lower bound of m1−δ is nearly tight.