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Computing boolean functions on anonymous networks

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Automata, Languages and Programming (ICALP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 443))

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Abstract

We study the bit-complexity of computing boolean functions on anonymous networks. Let N be the number of nodes, δ the diameter and d the maximal node degree of the network. For arbitrary, unlabeled networks we give a general algorithm of polynomial bit complexity O(N 4 · δ · d 2 · logN) for computing any boolean function which is computable on the network. This improves upon the previous best known algorithm which was of exponential bit complexity \(O(d^{N^2 } )\). For symmetric functions on arbitrary networks we give an algorithm with bit complexity O(N 2 · δ · d 2 · log2 N). This same algorithm is shown to have even lower bit complexity for a number of specific networks. We also consider the class of distance regular unlabeled networks and show that on such networks symmetric functions can be computed efficiently in O(N · δ · d · logN) bits.

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Author information

Authors and Affiliations

  1. Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB, Amsterdam, The Netherlands

    Evangelos Kranakis, Danny Krizanc & Jacob van den Berg

  2. Department of Computer Science, University of Rochester, 14627, Rochester, New York, USA

    Danny Krizanc

Authors
  1. Evangelos Kranakis
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  2. Danny Krizanc
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  3. Jacob van den Berg
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Editor information

Michael S. Paterson

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© 1990 Springer-Verlag Berlin Heidelberg

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Kranakis, E., Krizanc, D., van den Berg, J. (1990). Computing boolean functions on anonymous networks. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032037

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  • DOI: https://doi.org/10.1007/BFb0032037

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52826-5

  • Online ISBN: 978-3-540-47159-2

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