an:00751136
Zbl 0817.68019
Chlebus, Bogdan S.; Diks, Krzysztof; Pelc, Andrzej
Sparse networks supporting efficient reliable broadcasting
EN
Nord. J. Comput. 1, No. 3, 332-345 (1994).
00025784
1994
j
68M10 68Q25 90B18
broadcasting algorithms
Summary: Broadcasting concerns transmitting information from a node of a communication network to all other nodes. We consider this problem assuming that links and nodes of the network fail independently with given probabilities \(p < 1\) and \(q < 1\), respectively. For a positive constant \(\varepsilon\), broadcasting in an \(n\)-node network is said to be \(\varepsilon\)-safe, if source information is transmitted to all fault- free nodes with probability at least \(1 - n^{-\varepsilon}\). For any \(p < 1\), \(q < 1\) and \(\varepsilon > 0\) we show a class of \(n\)-node networks with maximum degree \(O (\log n)\) and \(\varepsilon\)-safe broadcasting algorithms for such networks working in logarithmic time.