Journal of Combinatorial Optimization

, Volume 14, Issue 2–3, pp 131–142 | Cite as

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

Article
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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.

Keywords

Multistage interconnection network Banyan network All-to-all communication All-to-all personalized exchange Latin square 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Victor W. Liu
    • 1
  • Chiuyuan Chen
    • 1
  • Richard B. Chen
    • 1
  1. 1.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan

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