Abstract
We consider the broadcasting problem in the shouting communication mode in which any node of a network can inform all its neighbors in one time step. In addition, during any time step a number of links less than the edge-connectivity of the network can be faulty. The problem is to find an upper bound on the number of time steps necessary to complete broadcasting under this additional assumption. Fraigniaud and Peyrat proved for the n-dimensional hypercube that n+ O( logn) time steps are sufficient. De Marco and Vaccaro decreased the upper bound to n+7 and showed a worst case lower bound n+2 for n≥3. We prove that n+2 time steps are sufficient. Our method is related to the isoperimetric problem in graphs and can be applied to other networks.
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