Combinatorica
Conductance and the rapid mixing property for Markov chains: the approximation of permanent resolved
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On the number of rounds necessary to disseminate information
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
How to withstand mobile virus attacks (extended abstract)
PODC '91 Proceedings of the tenth annual ACM symposium on Principles of distributed computing
Fast information sharing in a complete network
Discrete Applied Mathematics
Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Spreading rumors rapidly despite an adversary
PODC '96 Proceedings of the fifteenth annual ACM symposium on Principles of distributed computing
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Attack propagation in networks
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
An Efficient Communication Strategy for Ad-hoc Mobile Networks
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Distributed communication algorithms for ad hoc mobile networks
Journal of Parallel and Distributed Computing - Special issue on wireless and mobile ad hoc networking and computing
Mobile Networks and Applications
Infection spread in wireless networks with random and adversarial node mobilities
Proceedings of the 1st ACM SIGMOBILE workshop on Mobility models
Coverage-adaptive random walks for fast sensory data collection
ADHOC-NOW'10 Proceedings of the 9th international conference on Ad-hoc, mobile and wireless networks
A random walk model for infection on graphs: spread of epidemics & rumours with mobile agents
Discrete Event Dynamic Systems
Tight bounds on information dissemination in sparse mobile networks
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Random walks, interacting particles, dynamic networks: randomness can be helpful
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Viral processes by random walks on random regular graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Information spreading in dynamic graphs
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
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Consider k particles, 1 red and k - 1 white, chasing each other on the nodes of a graph G. If the red one catches one of the white, it "infects" it with its color. The newly red particles are now available to infect more white ones. When is it the case that all white will become red? It turns out that this simple question is an instance of information propagation between random walks and has important applications to mobile computing where a set of mobile hosts acts as an intermediary for the spread of information. In this paper we model this problem by k concurrent random walks, one corresponding to the red particle and k - 1 to the white ones. The infection time Tk of infecting all the white particles with red color is then a random variable that depends on k, the initial position of the particles, the number of nodes and edges of the graph, as well as on the structure of the graph. In this work we develop a set of probabilistic tools that we use to obtain upper bounds on the (worst case w.r.t. initial positions of particles) expected value of Tk for general graphs and important special cases. We easily get that an upper bound on the expected value of Tk is the worst case (over all initial positions) expected meeting time m* of two random walks multiplied by Θ(log k). We demonstrate that this is, indeed, a tight bound; i.e. there is a graph G (a special case of the "lollipop" graph), a range of values k n (such that √n - k = Θ(√n)) and an initial position of particles achieving this bound. When G is a clique or has nice expansion properties, we prove much smaller bounds for Tk. We have evaluated and validated all our results by large scale experiments which we also present and discuss here. In particular, the experiments demonstrate that our analytical results for these expander graphs are tight.