Finite State Model and Compatibility Theory: New Analysis Tools for Permutation Networks
IEEE Transactions on Computers
Fast Self-Routing Permutation Switching on an Asymptotically Minimum Cost Network
IEEE Transactions on Computers
A New Self-Routing Permutation Network
IEEE Transactions on Computers
Optimal All-to-All Personalized Exchange in Self-Routable Multistage Networks
IEEE Transactions on Parallel and Distributed Systems
Permutation capability of optical multistage interconnection networks: 72
Journal of Parallel and Distributed Computing
Performing Permutations on Interconnection Networks by Regularly Changing Switch States
IEEE Transactions on Parallel and Distributed Systems
Optimal All-to-All Personalized Exchange in a Class of Optical Multistage Networks
IEEE Transactions on Parallel and Distributed Systems
Introductory Combinatorics
Interconnection Networks: An Engineering Approach
Interconnection Networks: An Engineering Approach
IEEE Transactions on Parallel and Distributed Systems
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
On rearrangeability of tandem connection of banyan-type networks
IEEE Transactions on Communications
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Permutation is a frequently-used communication pattern in parallel and distributed computing systems and telecommunication networks. Node-disjoint routing has important applications in guided wave optical interconnects where the optical "crosstalk驴 between messages passing the same switch should be avoided. In this paper, we consider routing arbitrary permutations on an optical baseline network (or reverse baseline network) with node-disjoint paths. We first prove the equivalence between the set of admissible permutations (or semipermutations) of a baseline network and that of its reverse network based on a step-by-step permutation routing. We then show that an arbitrary permutation can be realized in a baseline network (or a reverse baseline network) with node-disjoint paths in four passes, which beats the existing results [5], [6] that a permutation can be realized in an n \times n Banyan network with node-disjoint paths in O(n^{\frac{1}{2}}) passes. This represents the currently best-known result for the number of passes required for routing an arbitrary permutation with node-disjoint paths in unique-path multistage networks. Unlike other unique path MINs (such as omega networks or Banyan networks), only baseline networks have been found to possess such four-pass routing property. We present routing algorithms in both self-routing style and central-controlled style. Different from the recent work in [21], which also gave a four-pass node-disjoint routing algorithm for permutations, the new algorithm is efficient in transmission time for messages of any length, while the algorithm in [21] can work efficiently only for long messages. Comparisons with previous results demonstrate that routing in a baseline network proposed in this paper could be a better choice for routing permutations due to its lowest hardware cost and near-optimal transmission time.