On the 1.1 edge-coloring of multigraphs
SIAM Journal on Discrete Mathematics
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
All-to-all routing and coloring in weighted trees of rings
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
The complexity of path coloring and call scheduling
Theoretical Computer Science
Approximation Algorithms and Complexity Results for Path Problems in Trees of Rings
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Efficient access to optical bandwidth
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A 2-approximation algorithm for path coloring on a restricted class of trees of rings
Journal of Algorithms
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Wavelength Assignment on Bounded Degree Trees of Rings
ICPADS '04 Proceedings of the Parallel and Distributed Systems, Tenth International Conference
Coloring all directed paths in a symmetric tree, with an application to optical networks
Journal of Graph Theory
An O (N2.5) algorithm for maximum matching in general graphs
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Efficient algorithms for wavelength assignment on trees of rings
Discrete Applied Mathematics
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Afundamental problem in communication networks is wavelength assignment(WA): given a set of routing paths on a network, assign a wavelength to each path such that the paths with the same wavelength are edge-disjoint, using the minimum number of wavelengths. The WA problem is NP-hard for a tree of rings network which is well used in practice. In this paper, we give an efficient algorithm which solves the WA problem on a tree of rings with an arbitrary (node) degree by at most 3Lwavelengths and achieves an approximation ratio of 2.75 asymptotically, where L is the maximum number of paths on any link in the network. The 3L upper bound is tight that there are instances of theWAproblem that require at least 3L wavelengths even on a tree of rings with degree four. We also give a 3L and 2-approximation algorithm for the WA problem on a tree of rings with degree at most six. Previous results include: 4L (resp. 3L) wavelengths for trees of rings with arbitrary degrees (resp. degree at most eight), and 2-approximation (resp. 2.5-approximation) algorithm for trees of rings with degree four (resp. six).