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Optimal all-to-all personalized exchange in d-nary banyan multistage interconnection networks

Author

Listed:
  • Victor W. Liu

    (National Chiao Tung University)

  • Chiuyuan Chen

    (National Chiao Tung University)

  • Richard B. Chen

    (National Chiao Tung University)

Abstract

All-to-all personalized exchange occurs in many important applications in parallel processing. In the past two decades, algorithms for all-to-all personalized exchange were mainly proposed for hypercubes, meshes, and tori. Recently, Yang and Wang (IEEE Trans Parallel Distrib Syst 11:261–274, 2000) proposed an optimal all-to-all personalized exchange algorithm for binary (each switch is of size 2×2) banyan multistage interconnection networks. It was pointed out in Massini (Discret Appl Math 128:435–446, 2003) that the algorithm in Yang, Wang (IEEE Trans Parallel Distrib Syst 11:261–274, 2000) depends on the network topologies and requires pre-computation and memory allocation for a Latin square. Thus in (Discret Appl Math 128:435–446, 2003), Massini proposed a new optimal algorithm, which is independent of the network topologies and does not require pre-computation or memory allocation for a Latin square. Unfortunately, Massini’s algorithm has a flaw and does not realize all-to-all personalized exchange. In this paper, we will correct the flaw and generalize Massini’s algorithm to be applicable to d-nary (each switch is of size d×d) banyan multistage interconnection networks.

Suggested Citation

  • Victor W. Liu & Chiuyuan Chen & Richard B. Chen, 2007. "Optimal all-to-all personalized exchange in d-nary banyan multistage interconnection networks," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 131-142, October.
    • Handle: RePEc:spr:jcomop:v:14:y:2007:i:2:d:10.1007_s10878-007-9065-5
    DOI: 10.1007/s10878-007-9065-5
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