Verifiable broadcasting and gossiping in communication networks
In network communication where messages may be corrupted in transmission, one way to verify the correctness of a given message is to arrange for nodes in the network to receive the message multiple times. For example, in broadcasting (one-to-all communication) from a given source node u, if a messag...
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Published in | Discrete Applied Mathematics Vol. 118; no. 3; pp. 293 - 298 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Lausanne
Elsevier B.V
15.05.2002
Amsterdam Elsevier New York, NY |
Subjects | |
Online Access | Get full text |
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Summary: | In network communication where messages may be corrupted in transmission, one way to verify the correctness of a given message is to arrange for nodes in the network to receive the message multiple times. For example, in
broadcasting (one-to-all communication) from a given source node
u, if a message sent by
u is received by all other nodes at least
k+1 times, then each node can perform
k checks against the original message to verify that it has not been corrupted in transmission. Similar behavior would be useful for
gossiping (all-to-all communication) where information held in each node is to be communicated to all other nodes. For an
n-node network, we consider the problem of determining the minimum number of network links required to support this
k-fold verifiability. We show that the minimum size
β(
n,
k) of an
n-vertex
k-verifiable broadcast scheme is given by
β(
n,
k)=⌈(
k+2)(
n−1)/2⌉. We also show that the minimum size
γ(
n,
k) of an
n-vertex
k-verifiable gossip scheme satisfies
⌈(k+4)(n−1)/2⌉−⌊
log
2
n⌋⩽γ(n,k)⩽⌈(k+4)n/2⌉−4
. The value for
β(
n,
k) and lower bound for
γ(
n,
k) yield lower bounds for the size of a
k-fault tolerant broadcast and gossip scheme which meet and improve, respectively, the previously known lower bounds for these schemes. |
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ISSN: | 0166-218X 1872-6771 |
DOI: | 10.1016/S0166-218X(00)00379-6 |