Tighter Worst-Case Bounds on Algebraic Gossip


Gossip and in particular network coded algebraic gossip have recently attracted attention as a fast, bandwidth-economical, reliable and distributed means to broadcast or multicast multiple messages. While the algorithms are easy, concerned queuing approaches are used to check their performance. The most recent end in this direction shows that uniform algebraic gossip disseminates k messages in O(Δ(D + k + log n)) rounds where D is that the diameter, n the size of the network and Δ the utmost degree. In this paper we tend to provide a simpler, short and self-contained proof for this worst-case guarantee. Our approach also allows to reduce the quadratic Δ D term to min3n, Δ D. We tend to furthermore show that a straightforward spherical robin routing scheme also achieves min3n, Δ D + Δ k rounds, eliminating both randomization and coding. Lastly, we have a tendency to combine a recent non-uniform gossip algorithm with a straightforward routing theme to induce a O(D + k + log^O(1)) gossip info dissemination algorithm. This is order optimal as long as D and k are not both polylogarithmically tiny.

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