Abstract
We consider the problem raised by Bassalygo: “What is the maximum number of rearrangements required by a rearrangeable 3-stage Clos network when there is an auxiliary middle switch carrying a light load?” For a 3-stage Clos network with an auxiliary middle switch carrying s connections, he claimed that the maximum number of rearrangements ϕ1 (n,n,r;s) 1 is less than \(s + \sqrt {2s } + 1\). In this paper, we give a lower bound 3×⌊s/2⌋ and an upper bound 2s + 1, where the lower bound shows that the upper bound given by Bassalygo does not hold in general.
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References
L.A. Bassalygo, On a number of reswitching in a three-stage connecting network, Inter. Teletraffic Cong. 7, pp. 231/1–231/4, 1973.
V.E. Benes, Mathematical Theory of Connecting Networks and Telephone Traffic, Academic, New York, 1965.
M.C. Paull, Reswitching of connection networks, Bell Syst. Tech. J. 4, pp. 833–855, 1962.
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© 1998 Springer-Verlag Berlin Heidelberg
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Hwang, F.K., Lin, WD. (1998). The Number of Rearrangements in a 3-stage Clos Network Using an Auxiliary Switch. In: Hsu, WL., Kao, MY. (eds) Computing and Combinatorics. COCOON 1998. Lecture Notes in Computer Science, vol 1449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68535-9_24
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DOI: https://doi.org/10.1007/3-540-68535-9_24
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