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Efficient dynamic embedding of arbitrary binary trees into hypercubes

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Parallel Algorithms for Irregularly Structured Problems (IRREGULAR 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1117))

Abstract

In this paper, a deterministic algorithm for dynamically embedding binary trees into next to optimal hypercubes is presented. Due to a known lower bound, any such algorithm must use either randomization or migration, i.e., remapping of tree vertices, to obtain an embedding of trees into hypercubes with small dilation, load, and expansion simultaneously. The algorithm presented here uses migration of previously mapped tree vertices and achieves dilation 9, unit load, expansion <4 and constant node-congestion. Moreover, the embedding can be computed on the hypercube. The amortized time for each new vertex is constant, if in each step one new leaf is spawned. If in each step a group of M new leaves is added, the amortized cost for each new group of leaves is bounded by O(log2(M)).

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Authors and Affiliations

  1. Institut für Informatik der Technischen Universität München, D-80290, München, Germany

    Volker Heun & Ernst W. Mayr

Authors
  1. Volker Heun
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  2. Ernst W. Mayr
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Editor information

Alfonso Ferreira José Rolim Yousef Saad Tao Yang

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© 1996 Springer-Verlag Berlin Heidelberg

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Heun, V., Mayr, E.W. (1996). Efficient dynamic embedding of arbitrary binary trees into hypercubes. In: Ferreira, A., Rolim, J., Saad, Y., Yang, T. (eds) Parallel Algorithms for Irregularly Structured Problems. IRREGULAR 1996. Lecture Notes in Computer Science, vol 1117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030119

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  • DOI: https://doi.org/10.1007/BFb0030119

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61549-1

  • Online ISBN: 978-3-540-68808-2

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