On the Role of Mobility for Multi-message Gossip

We consider information dissemination in a large $n$-user wireless network in which $k$ users wish to share a unique message with all other users. Each of the $n$ users only has knowledge of its own contents and state information; this corresponds to a one-sided push-only scenario. The goal is to disseminate all messages efficiently, hopefully achieving an order-optimal spreading rate over unicast wireless random networks. First, we show that a random-push strategy -- where a user sends its own or a received packet at random -- is order-wise suboptimal in a random geometric graph: specifically, $\Omega(\sqrt{n})$ times slower than optimal spreading. It is known that this gap can be closed if each user has "full" mobility, since this effectively creates a complete graph. We instead consider velocity-constrained mobility where at each time slot the user moves locally using a discrete random walk with velocity $v(n)$ that is much lower than full mobility. We propose a simple two-stage dissemination strategy that alternates between individual message flooding ("self promotion") and random gossiping. We prove that this scheme achieves a close to optimal spreading rate (within only a logarithmic gap) as long as the velocity is at least $v(n)=\omega(\sqrt{\log n/k})$. The key insight is that the mixing property introduced by the partial mobility helps users to spread in space within a relatively short period compared to the optimal spreading time, which macroscopically mimics message dissemination over a complete graph.Comment: accepted to IEEE Transactions on Information Theory, 201

Simple and Optimal Randomized Fault-Tolerant Rumor Spreading

We revisit the classic problem of spreading a piece of information in a group of $n$ fully connected processors. By suitably adding a small dose of randomness to the protocol of Gasienic and Pelc (1996), we derive for the first time protocols that (i) use a linear number of messages, (ii) are correct even when an arbitrary number of adversarially chosen processors does not participate in the process, and (iii) with high probability have the asymptotically optimal runtime of $O(\log n)$ when at least an arbitrarily small constant fraction of the processors are working. In addition, our protocols do not require that the system is synchronized nor that all processors are simultaneously woken up at time zero, they are fully based on push-operations, and they do not need an a priori estimate on the number of failed nodes. Our protocols thus overcome the typical disadvantages of the two known approaches, algorithms based on random gossip (typically needing a large number of messages due to their unorganized nature) and algorithms based on fair workload splitting (which are either not {time-efficient} or require intricate preprocessing steps plus synchronization).Comment: This is the author-generated version of a paper which is to appear in Distributed Computing, Springer, DOI: 10.1007/s00446-014-0238-z It is available online from http://link.springer.com/article/10.1007/s00446-014-0238-z This version contains some new results (Section 6

Improved Bounds on Information Dissemination by Manhattan Random Waypoint Model

With the popularity of portable wireless devices it is important to model and predict how information or contagions spread by natural human mobility -- for understanding the spreading of deadly infectious diseases and for improving delay tolerant communication schemes. Formally, we model this problem by considering $M$ moving agents, where each agent initially carries a \emph{distinct} bit of information. When two agents are at the same location or in close proximity to one another, they share all their information with each other. We would like to know the time it takes until all bits of information reach all agents, called the \textit{flood time}, and how it depends on the way agents move, the size and shape of the network and the number of agents moving in the network. We provide rigorous analysis for the \MRWP model (which takes paths with minimum number of turns), a convenient model used previously to analyze mobile agents, and find that with high probability the flood time is bounded by $O\big(N\log M\lceil(N/M) \log(NM)\rceil\big)$, where $M$ agents move on an $N\times N$ grid. In addition to extensive simulations, we use a data set of taxi trajectories to show that our method can successfully predict flood times in both experimental settings and the real world.Comment: 10 pages, ACM SIGSPATIAL 2018, Seattle, U