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Constructions of given-depth and optimal multirate rearrangeably nonblocking distributors

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Abstract

Rearrangeable multirate multicast switching networks are customarily called rearrangeable multirate distributors. It has been known for a long time that rearrangeable multirate distributors with cross-point complexity O(nlog 2 n) can be constructed, where n is the number of inputs (and outputs) of the switching network. The problem of constructing optimal distributors remains open thus far.

This paper gives a general construction of rearrangeable multirate distributors with given depths. One byproduct is a rearrangeable multirate distributor with crosspoint complexity O(nlog n). We also show that this cross-point complexity is optimal, settling the aforementioned open problem.

One of the key ingredients of our new construction is the notion of multirate concentrators. The second ingredient is a multirate version of the Pippenger network. We show how to construct given-depth multirate concentrators and given-depth multirate Pippenger networks with small sizes. When the depth is chosen to optimize the size, we obtain the optimal O(nlog n) cross-point complexity.

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Authors and Affiliations

  1. Computer Science and Engineering, State University of New York at Buffalo, 201 Bell Hall, Amherst, NY, 14260, USA

    Yang Wang, Hung Q. Ngo & Thanh-Nhan Nguyen

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  1. Yang Wang
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  2. Hung Q. Ngo
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  3. Thanh-Nhan Nguyen
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Correspondence to Hung Q. Ngo.

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Wang, Y., Ngo, H.Q. & Nguyen, TN. Constructions of given-depth and optimal multirate rearrangeably nonblocking distributors. J Comb Optim 24, 468–484 (2012). https://doi.org/10.1007/s10878-011-9402-6

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  • DOI: https://doi.org/10.1007/s10878-011-9402-6

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