Optimal Embeddings of the FFT Graph in the Hypercube

  • Authors:

  • David S. Greenberg;Lenwood S. Heath;Arnold L. Rosenberg

  • Affiliations:

  • -;-;-

  • Venue:
  • Optimal Embeddings of the FFT Graph in the Hypercube
  • Year:
  • 1988

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Abstract

WE PRESENT TWO LINEAR-TIME ALGORITHMS FOR EMBEDDING THE N-LEVEL `FFT'' GRAPH, WHICH HAS (N + 1)2(SUPERSCRIPT N) VERTICES, IN THE (N + [LOG(N + 1)])-DIMENSIONAL HYPERCUBE, WITH UNIT DILATION. THUS, THE `FFT'' GRAPH IS BIG ENOUGH TO HOLD IT. THE SIMPLER OF OUR ALGORITHMS USES GRAY CODES TO PERFORM THE EMBEDDING; THE MORE COMPLICATED HAS THE ADVANTAGE OF BEING MODULAR. EITHER EMBEDDING YIELDS A MAPPING OF THE `FFT'' ALGORITHM ONTO THE HYPERCUBE ARCHITECTURE, WITH UNIT (HENCE, OPTIMAL) DILATION AND OPTIMAL EXPANSION.