We also prove that for p = c lg lg lg n log nn, for any constant c > 16, a message held by any vertex of a Gn,p random graph can be broadcast to all other vertices in at most lgn + 1 time steps, with high probability. Integer sorting on multicores and GPUs can be realized by a variety of approaches that include variants of distribution-based methods such as radix-sort, comparison-oriented algorithms such as deterministic regular sampling and random sampling parallel sorting, and network-based algorithms such as Batcher’s bitonic sorting algorithm. It is assumed that at any time step a given vertex could either transmit to or receive from at most one other vertex one message in unit time.
We prove here that in Gn,p random graphs for the value of probability p used in Gerbessiotis, near-optimal broadcast can be achieved, with high probability, in llg n + O(lg lg lg n) time steps, an improvement over the previous time bound of lg n + O(lg lg n). Alexandros Gerbessiotis is a professor in the Computer Science department at New Jersey Institute of Technology - see what their students are saying about. Various results have been previously shown related to the minimum time needed to broadcast a message from any vertex to all the vertices of Gn,p random graphs. AbstractBroadcasting in random graphs has drawn increasing attention in the past years.
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