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

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


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.


Network State Stage Node Packing Algorithm Connection Request Switching Network 
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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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