Projects per year
Abstract
The asynchronous push&pull protocol, a randomized distributed algorithm for spreading a rumour in a graph G, is defined as follows. Independent exponential clocks of rate 1 are associated with the vertices of G, one to each vertex. Initially, one vertex of G knows the rumour. Whenever the clock of a vertex x rings, it calls a random neighbour y: if x knows the rumour and y does not, then x tells y the rumour (a push operation), and if x does not know the rumour and y knows it, y tells x the rumour (a pull operation). The average spread time of G is the expected time it takes for all vertices to know the rumour, and the guaranteed spread time of G is the smallest time t such that with probability at least 1 1=n, after time t all vertices know the rumour. The synchronous variant of this protocol, in which each clock rings precisely at times 1, 2, ..., has been studied extensively. We prove the following results for any nvertex graph: in either version, the average spread time is at most linear even if only the pull operation is used, and the guaranteed spread time is within a logarithmic factor of the average spread time, so it is O(n log n). In the asynchronous version, both the average and guaranteed spread times are (log n). We give examples of graphs illustrating that these bounds are best possible up to constant factors. We also prove the first theoretical relationships between the guaranteed spread times in the two versions. Firstly, in all graphs the guaranteed spread time in the asynchronous version is within an O(log n) factor of that in the synchronous version, and this is tight. Next, we find examples of graphs whose asynchronous spread times are logarithmic, but the synchronous versions are polynomially large. Finally, we show for any graph that the ratio of the synchronous spread time to the asynchronous spread time is O n2/3 .
Original language  English 

Title of host publication  Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (PODC'15) 
Editors  Paul G Spirakis 
Place of Publication  New York NY USA 
Publisher  Association for Computing Machinery (ACM) 
Pages  405412 
Number of pages  8 
ISBN (Print)  9781450336178 
DOIs  
Publication status  Published  2015 
Event  ACM Symposium on Principles of Distributed Computing 2015  Miramar Palace, DonostiaSan Sebastián, Spain Duration: 21 Jul 2015 → 23 Jul 2015 Conference number: 34th http://www.podc.org/podc2015/ 
Conference
Conference  ACM Symposium on Principles of Distributed Computing 2015 

Abbreviated title  PODC 2015 
Country/Territory  Spain 
City  DonostiaSan Sebastián 
Period  21/07/15 → 23/07/15 
Internet address 
Keywords
 Asynchronous time model
 Push & pull protocol
 Randomized rumour spreading
Projects
 2 Finished

Finite Markov chains in statistical mechanics and combinatorics
Garoni, T., Collevecchio, A. & Markowsky, G.
Australian Research Council (ARC)
2/01/14 → 31/12/17
Project: Research

Advances in the analysis of random structures and their applications: relationships among models
Australian Research Council (ARC)
1/08/12 → 31/12/17
Project: Research