Topological Properties of Hypercubes
IEEE Transactions on Computers
Proceedings of the 1990 ACM/IEEE conference on Supercomputing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
IEEE Transactions on Computers
Efficient collective communication in optical networks
Theoretical Computer Science
The congestion of n-cube layout on a rectangular grid
Discrete Mathematics - Special issue on Selected Topics in Discrete Mathematics conferences
Multicast routing and wavelength assignment in multihop optical networks
IEEE/ACM Transactions on Networking (TON)
IEEE Transactions on Parallel and Distributed Systems
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
Multihop All-to-All Broadcast on WDM Optical Networks
IEEE Transactions on Parallel and Distributed Systems
MPPOI '98 Proceedings of the The Fifth International Conference on Massively Parallel Processing Using Optical Interconnections
IEEE/ACM Transactions on Networking (TON)
Wavelength Assignment for Realizing Parallel FFT on Regular Optical Networks
The Journal of Supercomputing
Hypercube Computations on Partitioned Optical Passive Stars Networks
IEEE Transactions on Parallel and Distributed Systems
A general approach for all-to-all routing in multihop WDM optical networks
IEEE/ACM Transactions on Networking (TON)
On-line optimal wavelength assignment in WDM networks with shared wavelength converter pool
IEEE/ACM Transactions on Networking (TON)
Wavelength Assignment for Directional Hypercube Communications on a Class of WDM Optical Networks
ICPP '07 Proceedings of the 2007 International Conference on Parallel Processing
Routing and wavelength assignment for 3-ary n-cube in array-based optical network
Information Processing Letters
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Hypercube is one of the most versatile and efficient communication patterns shared by a large number of computational problems. As the number of edges in hypercube grows logarithmically with the size of networks, the complexity of network topologies can be significantly reduced to realize hypercube in optical networks by taking advantage of the parallel transmission characteristic of optical fibers. In this paper, we study the routing and wavelength assignment for realizing hypercube on WDM optical networks including linear arrays and rings with the consideration of communication directions. Specifically, we analyze this problem for both bidirectional and unidirectional hypercubes. For each case, we identify a lower bound on the number of wavelengths required, and design the embedding scheme and wavelength assignment algorithm that uses a provably near-optimal number of wavelengths. In addition, we extend the results to meshes and tori. By our embedding schemes, many algorithms, originally designed based on hypercubes, can be applied to optical networks, and the wavelength requirements can be easily derived using our obtained results.