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Study of Wide-sense Nonblocking Switching Networks from the Approach of Upper Ideals

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Part of the Network Theory and Applications book series (NETA, volume 5)

Abstract

A switching network is said to be wide-sense nonblocking if there is a non-blocking algorithm for route selection. In 1965, Bereš [1] proved the 3-stage Clos network [n×m, 2×2, m×n] to be nonblocking when \( m \geqslant \left\lfloor {\tfrac{{3n}} {2}} \right\rfloor \). This identified a family of 3-stage networks that are wide-sense nonblocking but not strictly nonblocking. It also raised the question on the existence of any wide-sense nonblocking network [n×m, r × r, m×n], r > 2, that is not strictly nonblocking. We answer this question affirmatively with an algorithm over the network [6×10, 3×3, 10×6]. We also prove that, if a certain packing algorithm over [n×m, 3×3, m×n] is nonblocking, then \( m \geqslant \left\lfloor {\tfrac{{15n}} {8}} \right\rfloor \). Consequently a wide-sense nonblocking network does not necessarily admit a packing algorithm.

Keywords

Network State Stage Node Packing Algorithm Connection Request Switching Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Department of Information EngineeringThe Chinese University of Hong KongHong KongChina

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