A guided tour of Chernoff bounds
Information Processing Letters
Dynamic Perfect Hashing: Upper and Lower Bounds
SIAM Journal on Computing
Methods and problems of communication in usual networks
Proceedings of the international workshop on Broadcasting and gossiping 1990
Efficient gossiping by packets in networks with random faults
SIAM Journal on Discrete Mathematics
Chernoff-Hoeffding bounds for applications with limited independence
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
PRAM Computations Resilient to Memory Faults
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
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Every node of a network has a value which should be made known to all the other nodes. Some arbitrarily placed nodes and links may be faulty, however for each pair of fault-free nodes the number of fault-free paths of length 2 that connect them is linear in the size of the network. Faults are of crash type: faulty links do not transmit and faulty nodes neither send nor receive messages. In a unit of time a node can send or receive at most one packet containing the values of at most b nodes. For every 1 驴 b 驴 n we present an asymptotically time-optimal randomized algorithm to exchange values between all the fault-free nodes with the probability exceeding 1 - n-驴, where n is the number of nodes and 驴 0 is an arbitrary constant.