Low Randomness Rumor Spreading via Hashing

We consider the classical rumor spreading problem, where a piece of information must be disseminated from a single node to all n nodes of a given network. We devise two simple push-based protocols, in which nodes choose the neighbor they send the information to in each round using pairwise independent hash functions, or a pseudo-random generator, respectively. For several well-studied topologies our algorithms use exponentially fewer random bits than previous protocols. For example, in complete graphs, expanders, and random graphs only a polylogarithmic number of random bits are needed in total to spread the rumor in O(log n) rounds with high probability. Previous explicit algorithms, e.g., [6, 10, 15, 17], require Ω(n) random bits to achieve the same round complexity. For complete graphs, the amount of randomness used by our hashing-based algorithm is within an O(log n)-factor of the theoretical minimum determined by Giakkoupis and Woelfel [15]. 1998 ACM Subject Classification G.3...

• Type: Journal
• Year: 2012
• Where: STACS
• Authors: George Giakkoupis, Thomas Sauerwald, He Sun, Philipp Woelfel
• Keywords: Probability And Statistics, Pseudo Random Generator, Random Graphs, STACS 2012, Theoretical Computer Science