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Fast algorithms for bit-serial routing on a hypercube

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Abstract

In this paper we describe anO(logN)-bit-step randomized algorithm for bit-serial message routing on a hypercube. The result is asymptotically optimal, and improves upon the best previously known algorithms by a logarithmic factor. The result also solves the problem of on-line circuit switching in anO(1)-dilated hypercube (i.e., the problem of establishing edge-disjoint paths between the nodes of the dilated hypercube for any one-to-one mapping).

Our algorithm is adaptive and we show that this is necessary to achieve the logarithmic speedup. We generalize the Borodin-Hopcroft lower bound on oblivious routing by proving that any randomized oblivious algorithm on a polylogarithmic degree network requires at least Ω(log2 N/log logN) bit steps with high probability for almost all permutations.

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Author information

Authors and Affiliations

  1. Bell Communications Research, 07960, Morristown, NJ, USA

    William A. Aiello

  2. Mathematics Department and Laboratory for Computer Science, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    F. T. Leighton

  3. NEC Research Institute, 08540, Princeton, NJ, USA

    Bruce M. Maggs

  4. Temple Barker and Sloane Inc., 02173, Lexington, MA, USA

    Mark Newman

Authors
  1. William A. Aiello
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  2. F. T. Leighton
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  3. Bruce M. Maggs
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  4. Mark Newman
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Additional information

This research was supported by the Defense Advanced Research Projects Agency under Contracts N00014-87-K-825 and N00014-89-J-1988, the Air Force under Contract AFOSR-89-0271, and the Army under Contract DAAL-03-86-K-0171. This work was completed while the third and fourth authors were at the Laboratory for Computer Science, Massachusetts Institute of Technology.

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Aiello, W.A., Leighton, F.T., Maggs, B.M. et al. Fast algorithms for bit-serial routing on a hypercube. Math. Systems Theory 24, 253–271 (1991). https://doi.org/10.1007/BF02090402

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  • DOI: https://doi.org/10.1007/BF02090402

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