Distributed loop computer networks: a survey
Journal of Parallel and Distributed Computing
All-to-all routing and coloring in weighted trees of rings
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
All-to-all optical routing in optimal chordal rings of degree four
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Efficient Collective Communication in Optical Networks
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Colouring Paths in Directed Symmetric Trees with Applications to WDM Routing
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
A new look at fault tolerant network routing
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Graph Theory With Applications
Graph Theory With Applications
Multi-hop all-to-all optical routings in Cartesian product networks
Information Processing Letters
Wavelength routing of uniform instances in all-optical rings
Discrete Optimization
Reliable collective communications with weighted SRLGs in optical networks
IEEE/ACM Transactions on Networking (TON)
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We consider all-to-all routing problem in an optical ring network that uses the wavelength-division multiplexing (WDM). Since 1-hop, all-to-all optical routing in a WDM optical ring of n nodes needs ⌈½⌊n2/4⌋⌉ wavelengths (see Efficient Collective Communication in Optical Networks, Lecture Notes in Computer Science, Vol. 1099, Springer, Berlin, 1996, pp. 574-585), which can be too large even for moderate values of n, we consider in this paper j-hop implementations of all-to-all routing in a WDM optical ring, j ≥ 2. From among the possible routings we focus our attention on uniform routings, in which each node of the ring uses the same communication pattern and the communication load is distributed evenly among the nodes. We show that there exists a uniform 2-hop implementation of all-to-all routing that needs at most (n/4)(3√n+ 3) wavelengths. This value is within multiplicative constants of a lower bound. We then give a uniform 3-hop, 4-hop implementation of all-to-all routing that needs at most (n/2)(7√n/16 + 3), (n/2)(15√n/2 + 6) wavelengths, respectively.