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• W2014394992 abstract "In this paper we study gossip based information spreading with bounded message sizes. We use algebraic gossip to disseminate $$k$$ distinct messages to all $$n$$ nodes in a network. For arbitrary networks we provide a new upper bound for uniform algebraic gossip of $$O((k+log n + D)varDelta )$$ rounds with high probability, where $$D$$ and $$varDelta $$ are the diameter and the maximum degree in the network, respectively. For many topologies and selections of $$k$$ this bound improves previous results, in particular, for graphs with a constant maximum degree it implies that uniform gossip is order optimal and the stopping time is $$varTheta (k + D)$$ . To eliminate the factor of $$varDelta $$ from the upper bound we propose a non-uniform gossip protocol, TAG, which is based on algebraic gossip and an arbitrary spanning tree protocol $$mathcal{S } $$ . The stopping time of TAG is $$O(k+log n +d(mathcal{S })+t(mathcal{S }))$$ , where $$t(mathcal{S })$$ is the stopping time of the spanning tree protocol, and $$d(mathcal{S })$$ is the diameter of the spanning tree. We provide two general cases in which this bound leads to an order optimal protocol. The first is for $$k=varOmega (n)$$ , where, using a simple gossip broadcast protocol that creates a spanning tree in at most linear time, we show that TAG finishes after $$varTheta (n)$$ rounds for any graph. The second uses a sophisticated, recent gossip protocol to build a fast spanning tree on graphs with large weak conductance. In turn, this leads to the optimally of TAG on these graphs for $$k=varOmega (text{ polylog }(n))$$ . The technique used in our proofs relies on queuing theory, which is an interesting approach that can be useful in future gossip analysis." @default.
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• W2014394992 date "2013-04-01" @default.
• W2014394992 modified "2023-09-23" @default.
• W2014394992 title "Order optimal information spreading using algebraic gossip" @default.
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• W2014394992 doi "https://doi.org/10.1007/s00446-013-0187-y" @default.
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