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Constructions of given-depth and optimal multirate rearrangeably nonblocking distributors

Author

Listed:
  • Yang Wang

    (State University of New York at Buffalo)

  • Hung Q. Ngo

    (State University of New York at Buffalo)

  • Thanh-Nhan Nguyen

    (State University of New York at Buffalo)

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.

Suggested Citation

  • Yang Wang & Hung Q. Ngo & Thanh-Nhan Nguyen, 2012. "Constructions of given-depth and optimal multirate rearrangeably nonblocking distributors," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 468-484, November.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:4:d:10.1007_s10878-011-9402-6
    DOI: 10.1007/s10878-011-9402-6
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