Deterministic sorting in nearly logarithmic time on the hypercube and related computers
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
An introduction to parallel algorithms
An introduction to parallel algorithms
Optical networks: a practical perspective
Optical networks: a practical perspective
The Mathematical Theory of Nonblocking Switching Networks
The Mathematical Theory of Nonblocking Switching Networks
Proceedings of the Sagamore Computer Conference on Parallel Processing
Graph Theory With Applications
Graph Theory With Applications
Optical multistage interconnection networks: new challenges and approaches
IEEE Communications Magazine
Wide-sense nonblocking Banyan-type switching systems based on directional couplers
IEEE Journal on Selected Areas in Communications
A comparison study of optical MIN networks with parallel planes
PDCN'06 Proceedings of the 24th IASTED international conference on Parallel and distributed computing and networks
A practical fast parallel routing architecture for Clos networks
Proceedings of the 2006 ACM/IEEE symposium on Architecture for networking and communications systems
A novel design of self-routing strictly nonblocking switching networks
International Journal of Computers and Applications
A parallel self-routing rearrangeable nonblocking multi-log2 N photonic switching network
IEEE/ACM Transactions on Networking (TON)
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We study the connection capacity of a class of rearrangeable nonblocking (RNB) and strictly nonblocking (SNB) networks with/without crosstalk-free constraint, model their routing problems as weak or strong edge-colorings of bipartite graphs, and propose efficient routing algorithms for these networks using parallel processing techniques. This class of networks includes networks constructed from Banyan networks by horizontal concatenation of extra stages and/or vertical stacking of multiple planes. We present a parallel algorithm that runs in O(\lg^2 N) time for the RNB networks of complexities ranging from O(N\lg N) to O(N^{1.5}\lg N) crosspoints and parallel algorithms that run in O(\min \{d^*\lg N, \sqrt{N}\}) time for the SNB networks of O(N^{1.5}\lg N) crosspoints, using a completely connected multiprocessor system of N processing elements. Our algorithms can be translated into algorithms with an O(\lg N \lg\lg N) slowdown factor for the class of N{\hbox{-}}{\rm{processor}} hypercubic networks, whose structures are no more complex than a single plane in the RNB and SNB networks considered.