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Computing boolean functions on anonymous networks

  • Evangelos Kranakis
  • Danny Krizanc
  • Jacob van den Berg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 443)

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(N4 · δ · d2 · 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(N2 · δ · d2 · log2N). 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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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Evangelos Kranakis
    • 1
  • Danny Krizanc
    • 1
    • 2
  • Jacob van den Berg
    • 1
  1. 1.Centre for Mathematics and Computer ScienceAmsterdamThe Netherlands
  2. 2.Department of Computer ScienceUniversity of RochesterRochesterUSA

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