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Reliable Broadcasting in Hypercubes with Random Link and Node Failures

Published online by Cambridge University Press:  12 September 2008

Bogdan S. Chlebus ,
Krzysztof Diks  and
Andrzej Pelc
Bogdan S. Chlebus
Affiliation:
Instytut Informatyki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa, Poland
Krzysztof Diks
Affiliation:
Instytut Informatyki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa, Poland
Andrzej Pelc
Affiliation:
Département d'Informatique, Université du Québec à Hull, C.P. 1250, succ. ‘B’, Hull, Québec J8X 3X7, Canada
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Abstract

We consider the problem of broadcasting in an n–node hypercube whose links and nodes fail independently with given probabilities p < 1 and q < 1, respectively. Information held in a fault-free node, called the source, has to reach all other fault-free nodes. Messages may be directly transmitted to adjacent nodes only, and every node may communicate with at most one neighbour in a unit of time. A message can be transmitted only if both communicating neighbours and the link joining them are fault-free. For parameters p and q satisfying (1 – p)(1 – q) ≽ 0.99 (e.g. p = q = 0.5%), we give an algorithm working in time O(log n) and broadcasting source information to all fault-free nodes with probability exceeding 1 – cn-e for some positive constant ε, c depending on p and q but not depending on n.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 4 , December 1996 , pp. 337 - 350
Copyright
Copyright © Cambridge University Press 1996

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