Coding Theory 1988: Coding Theory and Applications pp 213-225 | Cite as

Covering in hypercubes

  • Arif Ghafoor
  • Patrick Solé
Section III Combinatorial And Algebraic Aspects
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 388)

Abstract

In this paper we propose a semi-distributed self-diagnostic algorithm for Hypercube networks which is based on the use of a combinatorial structure known as the Hadamard matrix. We propose a model for providing fault- tolerance to the diagnostic scheme and to analyze the performance of the proposed diagnostic scheme. This analysis provides a tradeoff between the complexity of the algorithm and its level of fault-tolerance. However, the optimal solution to the diagnostic problem with desired level of fault- tolerance is shown to be related to the problem of finding the covering radius of a binary code which is a NP-hard problem for the Hypercube networks. We discuss various cases for n=8, 16, 32. However, for achieving a level of about 50% fault-tolerance for the proposed diagnostic scheme, we provide an optimal solution valid for all Hypercube networks.

Keywords

Diagnostic Scheme Graphical Distance Hadamard Matrice Hadamard Matrix Faulty Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Arif Ghafoor
    • 1
  • Patrick Solé
    • 2
  1. 1.Dept. of Electrical and Computer Engr.Syracuse UniversitySyracuse
  2. 2.School of Computer and Information ScienceSyracuse University

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