SIAM Journal on Applied Mathematics
A guided tour of Chernoff bounds
Information Processing Letters
Adaptive broadcasting with faulty nodes
Parallel Computing
The Mathematics of Infectious Diseases
SIAM Review
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Dissemination of Information in Communication Networks: Broadcasting, Gossiping, Leader Election, and Fault-Tolerance (Texts in Theoretical Computer Science. An EATCS Series)
Agent-based randomized broadcasting in large networks
Discrete Applied Mathematics
Broadcasting vs. mixing and information dissemination on Cayley graphs
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On randomized broadcasting in star graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Efficient broadcast on random geometric graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
How efficient can gossip be? (on the cost of resilient information exchange)
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Rumor spreading on random regular graphs and expanders
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
On the randomness requirements of rumor spreading
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Diameter and broadcast time of random geometric graphs in arbitrary dimensions
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
The worst case behavior of randomized gossip
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Strong robustness of randomized rumor spreading protocols
Discrete Applied Mathematics
Randomized information dissemination in dynamic environments
IEEE/ACM Transactions on Networking (TON)
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In this paper, we study the following randomized broadcasting protocol. At some time t an information r is placed at one of the nodes of a graph. In the succeeding steps, each informed node chooses one neighbor, independently and uniformly at random, and informs this neighbor by sending a copy of r to it. We begin by developing tight lower and upper bounds on the runtime of the algorithm described above. First, it is shown that on @D-regular graphs this algorithm requires at least log"2"-"1"@Dn+log"("@D"@D"-"1")"^"@Dn-o(logn)~1.69log"2n rounds to inform all n nodes. Together with a result of Pittel [B. Pittel, On spreading a rumor, SIAM Journal on Applied Mathematics, 47 (1) (1987) 213-223] this bound implies that the algorithm has the best performance on complete graphs among all regular graphs. For general graphs, we prove a slightly weaker lower bound of log"2"-"1"@Dn+log"4n-o(logn)~1.5log"2n, where @D denotes the maximum degree of G. We also prove two general upper bounds, (1+o(1))nlnn and O(n@D@d), respectively, where @d denotes the minimum degree. The second part of this paper is devoted to the analysis of fault-tolerance. We show that if the informed nodes are allowed to fail in some step with probability 1-p, then the broadcasting time increases by at most a factor 6/p. As a by-product, we determine the performance of agent based broadcasting in certain graphs and obtain bounds for the runtime of randomized broadcasting on Cartesian products of graphs.