The main result is a simple randomized algorithm called median rule that, with high probability, just needs O(log m log log n + log n) time and work per process to arrive at an almost stable consensus for any set of m legal values as long as an adversary can corrupt the states of at most √n processes at any time.Expand

Surprisingly, it is able to show that, if 2 < β < 3, the rumor spreads even in constant time, which is much smaller than the typical distance of two nodes, and the first result that establishes a gap between the synchronous and the asynchronous protocol.Expand

This work investigates several randomized protocols for different communication models in the discrete case of discrete load balancing and demonstrates that there is almost no difference between the discrete and continuous case.Expand

It is proved that the speed-up is ${\mathcal{O}}(k \log n)$ on any graph, and a surprisingly sharp dichotomy on several graphs (including d -dim) is revealed.Expand

A quasirandom analogue to the classical push model for disseminating information in networks ("randomized rumor spreading") that achieves similar or better broadcasting times with a greatly reduced use of random bits.Expand

It is shown that for any two nodes sufficiently distant from each other in [0, √<i>n</i>]<sup>2</sup>, the length of the shortest path between them in the RGG, when such a path exists, is only a constant factor larger than the optimum.Expand

It is shown that first-passage probabilities of a random walk on a path with arbitrary weights can be expressed as a convolution of independent geometric probability distributions and the quasirandom algorithm is the first known algorithm for this setting which is optimal both in time and achieved smoothness.Expand

Two allocation schemes are analyzed that achieve a close to optimal maximum load of ⌈m/n⌉ + 1 and require only O(m) (expected) allocation time and are compared with the classic d-choice-process.Expand

It is proved that w.h.p. is the diameter of the largest connected component of an RGG within Θ(n1/d/r+logn) rounds, and that for any two connected nodes with a minimum Euclidean distance of ω(logn), their graph distance is only a constant factor larger than their Euclidan distance.Expand