TY - GEN

T1 - Tight bounds for algebraic gossip on graphs

AU - Borokhovich, Michael

AU - Avin, Chen

AU - Lotker, Zvi

PY - 2010

Y1 - 2010

N2 - We study the stopping times of gossip algorithms for network coding. We analyze algebraic gossip (i.e., random linear coding) and consider three gossip algorithms for information spreading Pull, Push, and Exchange. The stopping time of algebraic gossip is known to be linear for the complete graph, but the question of determining a tight upper bound or lower bounds for general graphs is still open. We take a major step in solving this question, and prove that algebraic gossip on any graph of size n is O(Δn) where Δ is the maximum degree of the graph. This leads to a tight bound of θ(n) for bounded degree graphs and an upper bound of O(n2) for general graphs. We show that the latter bound is tight by providing an example of a graph with a stopping time of Ω (n2). Our proofs use a novel method that relies on Jackson's queuing theorem to analyze the stopping time of network coding; this technique is likely to become useful for future research.

AB - We study the stopping times of gossip algorithms for network coding. We analyze algebraic gossip (i.e., random linear coding) and consider three gossip algorithms for information spreading Pull, Push, and Exchange. The stopping time of algebraic gossip is known to be linear for the complete graph, but the question of determining a tight upper bound or lower bounds for general graphs is still open. We take a major step in solving this question, and prove that algebraic gossip on any graph of size n is O(Δn) where Δ is the maximum degree of the graph. This leads to a tight bound of θ(n) for bounded degree graphs and an upper bound of O(n2) for general graphs. We show that the latter bound is tight by providing an example of a graph with a stopping time of Ω (n2). Our proofs use a novel method that relies on Jackson's queuing theorem to analyze the stopping time of network coding; this technique is likely to become useful for future research.

UR - http://www.scopus.com/inward/record.url?scp=77955685151&partnerID=8YFLogxK

U2 - 10.1109/isit.2010.5513272

DO - 10.1109/isit.2010.5513272

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AN - SCOPUS:77955685151

SN - 9781424469604

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1758

EP - 1762

BT - 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings

T2 - 2010 IEEE International Symposium on Information Theory, ISIT 2010

Y2 - 13 June 2010 through 18 June 2010

ER -