Solving problems on concurrent processors
Solving problems on concurrent processors
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Optical computer architectures: the application of optical concepts to next generation computers
Optical computer architectures: the application of optical concepts to next generation computers
Methods and problems of communication in usual networks
Proceedings of the international workshop on Broadcasting and gossiping 1990
Efficient routing in optical networks
Journal of the ACM (JACM)
All-to-all routing and coloring in weighted trees of rings
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
On scheduling all-to-all personalized connections and cost-effective designs in WDM rings
IEEE/ACM Transactions on Networking (TON)
Ring routing and wavelength translation
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
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
Theoretical Computer Science
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
Uniform Multi-hop All-to-All Optical Routings in Rings
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Optical All-to-All Communication for Some Product Graphs
SOFSEM '97 Proceedings of the 24th Seminar on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Multihop All-to-All Broadcast on WDM Optical Networks
IEEE Transactions on Parallel and Distributed Systems
A new look at fault tolerant network routing
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Optimization of logical rings for multi-hop transmissions in WDM optical star networks
Computer Communications
Multi-hop all-to-all optical routings in Cartesian product networks
Information Processing Letters
Routing and wavelength assignment for hypercube in array-based WDM optical networks
Journal of Parallel and Distributed Computing
Wavelength assignment for all-to-all broadcast in WDM optical linear array with limited drops
Computer Communications
Reliable collective communications with weighted SRLGs in optical networks
IEEE/ACM Transactions on Networking (TON)
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WDM optical networks provide unprecedented high speed and reliability for message transfer among the nodes. All-to-all routing is a fundamental routing problem in such networks and has been well studied on single hop WDM networks. However, the number of wavelengths to realize all-to-all routing on the single hop model typically is very large. One way to reduce the number of wavelengths is to use k-hop routing, in which each routing path consists of k segments and each segment is assigned a different wavelength, where k usually is a small constant. Because of the complexity of design and analysis for such a routing problem, only few papers discussed and proposed all-to-all routing by k ≥ 2 hops. However, the proposed algorithms are usually exceeding complicated even for ring topologies. Often, an ad hoc approach is employed to deal with each individual topology.In this paper we propose a generic method for all-to-all routing in multi-hop WDM networks, which aims to minimize the number of wavelengths. We illustrate the approach for several optical networks of commonly used topology, including lines, rings, tori, meshes, and complete binary trees. For each case an upper bound on the number of wavelengths is obtained. The results show that this approach produces clear routing paths, requires less wavelengths, and can easily incorporate load balancing. For simple topologies such as lines and rings, this approach easily produces the same bounds on the number of wavelengths that were hard-obtained previously. Moreover, this general approach provides a unified routing algorithm for any d-dimensional torus, which seems impossible to obtain by the previous approach.