TY - GEN

T1 - Order optimal information spreading using algebraic gossip

AU - Avin, Chen

AU - Borokhovich, Michael

AU - Censor-Hillel, Keren

AU - Lotker, Zvi

PY - 2011

Y1 - 2011

N2 - 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)Δ) rounds with high probability, where D and Δ 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 θ(k + D). To eliminate the factor of Δ from the upper bound we propose a non-uniform gossip protocol, TAG, which is based on algebraic gossip and an arbitrary spanning tree protocol S. The stopping time of TAG is O(k+ log n + d(S) + t(S)), where t(S) is the stopping time of the spanning tree protocol, and d(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=Ω(n), where, using a simple gossip broadcast protocol that creates a spanning tree in at most linear time, we show that TAG finishes after θ(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=Ω(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.

AB - 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)Δ) rounds with high probability, where D and Δ 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 θ(k + D). To eliminate the factor of Δ from the upper bound we propose a non-uniform gossip protocol, TAG, which is based on algebraic gossip and an arbitrary spanning tree protocol S. The stopping time of TAG is O(k+ log n + d(S) + t(S)), where t(S) is the stopping time of the spanning tree protocol, and d(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=Ω(n), where, using a simple gossip broadcast protocol that creates a spanning tree in at most linear time, we show that TAG finishes after θ(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=Ω(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.

KW - algebraic gossip

KW - gossip

KW - network coding

KW - tight bounds

UR - http://www.scopus.com/inward/record.url?scp=79959900070&partnerID=8YFLogxK

U2 - 10.1145/1993806.1993883

DO - 10.1145/1993806.1993883

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AN - SCOPUS:79959900070

SN - 9781450307192

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 363

EP - 371

BT - PODC'11 - Proceedings of the 2011 ACM Symposium Principles of Distributed Computing

T2 - 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC'11, Held as Part of the 5th Federated Computing Research Conference, FCRC

Y2 - 6 June 2011 through 8 June 2011

ER -