Broadcasting in Partially Ordered Sets
نویسنده
چکیده
Let be a partial order on a countable set V such that there exists a minimum element a ∈ V and {u ∈ V : u v} is finite for each v ∈ V . An item of information is to be broadcast to the elements of V according to the policy in the following sense: a is initially informed and broadcasting to v 6= a begins as soon as all elements u ≺ v are informed; the time required to broadcast the information is X(v) where {X(v) : v 6= a} is a collection of independent, identically distributed variables with mean 1. The natural random variables associated with this model are the time required to broadcast the information to a given set of vertices and the set of informed vertices at a given time. These variables are studied in terms of the structure of the directed graph associated with . A number of stochastic comparison results are obtained. The common model for deterministic broadcasting in trees is a special case.
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تاریخ انتشار 2000