Abstract
Concentrators are interconnection networks that provide vertex-disjoint directed paths to satisfy interconnection requests. An interconnection network is non-blocking in the strict sense if every compatible interconnection request can be satisfied regardless of any existing interconnections. We show a size optimal bound of Θ(n 1+1/k) for synchronous strictly non-blocking γn-limited (αn, βn)-concentrators with non-full capacity and constant depth k, and present a size upper bound of O(n 1+1/⌈k/2⌉) for synchronous strictly non-blocking βn-limited (αn, βn)-concentrators with full capacity and constant depth k.
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Dai, H.K. (1996). The size complexity of strictly non-blocking fixed ratio concentrators with constant depth. In: Bougé, L., Fraigniaud, P., Mignotte, A., Robert, Y. (eds) Euro-Par'96 Parallel Processing. Euro-Par 1996. Lecture Notes in Computer Science, vol 1123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61626-8_30
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DOI: https://doi.org/10.1007/3-540-61626-8_30
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