Asymptotically Optimal Randomized Rumor Spreading

Abstract

Abstract We propose a new protocol for the fundamental problem of disseminating a piece of information to all members of a group of n players. It builds upon the classical randomized rumor spreading protocol and several extensions. The main achievements are the following: Our protocol spreads a rumor from one node to all other nodes in the asymptotically optimal time of ( 1 + o ( 1 ) ) log 2 n . The whole process makes only O ( nf ( n )) calls, where f ( n ) = ω ( 1 ) can be arbitrary. In spite of these quantities being close to the theoretical optima, the protocol remains relatively robust against failures. We show that for random node failures, our algorithm again comes arbitrarily close to the theoretical optima. The protocol can be extended to also deal with adversarial node failures. The price for this additional robustness is only a constant factor increase in the run-time, where the constant factor depends on the fraction of failing nodes the protocol is supposed to cope with. Still only O ( n ) calls to properly working nodes are made. In contrast to the push-pull protocol by Karp et al. [FOCS 2000], our algorithm only uses push operations. To the best of our knowledge, this is the first randomized push algorithm that achieves an asymptotically optimal running time.