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Optimal specified root embedding of full binary trees in faulty hypercubes

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ISA'91 Algorithms (ISA 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 557))

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Abstract

We study the problem of running full binary tree based algorithms on a hypercube with faulty nodes. The key to this problem is to devise an algorithm for embedding a full binary tree in the faulty hypercube. Supposing that the root of the tree must be mapped to a specified hypercube node, we show how to embed an (n−1)-tree (a full binary tree with 2n−1-1 nodes) into an n-cube (a hypercube with 2n nodes) having up to n−2 faults. Our embedding has unit dilation and load, and the result is optimal in the sense that the algorithm is time-optimal, the (n−1)-tree is the largest full binary tree that can be embedded in an n-cube, and n−2 faults is the maximum number of faults that can be tolerated when the root is fixed. Furthermore, we also show that any algorithm for this problem cannot be totally recursive in nature.

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Authors and Affiliations

  1. Department of Computer Science, University of Hong Kong, Hong Kong

    M. Y. Chan, F. Y. L. Chin & C. K. Poon

Authors
  1. M. Y. Chan
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  2. F. Y. L. Chin
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  3. C. K. Poon
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Editor information

Wen-Lian Hsu R. C. T. Lee

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© 1991 Springer-Verlag Berlin Heidelberg

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Chan, M.Y., Chin, F.Y.L., Poon, C.K. (1991). Optimal specified root embedding of full binary trees in faulty hypercubes. In: Hsu, WL., Lee, R.C.T. (eds) ISA'91 Algorithms. ISA 1991. Lecture Notes in Computer Science, vol 557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54945-5_68

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  • DOI: https://doi.org/10.1007/3-540-54945-5_68

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54945-1

  • Online ISBN: 978-3-540-46600-0

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