A stochastic process on the hypercube with applications to peer-to-peer networks
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Conductance and congestion in power law graphs
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
On the spread of viruses on the internet
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Random walk based node sampling in self-organizing networks
ACM SIGOPS Operating Systems Review
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Many random walks are faster than one
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Conductance and convergence of Markov chains-a combinatorial treatment of expanders
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Generating random spanning trees
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Tight Bounds for the Cover Time of Multiple Random Walks
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Proceedings of the 28th ACM symposium on Principles of distributed computing
How Well Do Random Walks Parallelize?
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Almost tight bounds for rumour spreading with conductance
Proceedings of the forty-second ACM symposium on Theory of computing
Efficient distributed random walks with applications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Speeding up random walks with neighborhood exploration
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Rumour spreading and graph conductance
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Rumor spreading on random regular graphs and expanders
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
A random walk model for infection on graphs: spread of epidemics & rumours with mobile agents
Discrete Event Dynamic Systems
A tight upper bound on the cover time for random walks on graphs
Random Structures & Algorithms
A tight lower bound on the cover time for random walks on graphs
Random Structures & Algorithms
Rumor spreading in social networks
Theoretical Computer Science
Rumor spreading and vertex expansion
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Ultra-fast rumor spreading in social networks
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Optimal cover time for a graph-based coupon collector process
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The N-intertwined SIS epidemic network model
Computing - Special Issue on Bio inspired Computing
Random walks in distributed computing: a survey
IICS'04 Proceedings of the 4th international conference on Innovative Internet Community Systems
Coalescing random walks and voting on graphs
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
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We study a distributed randomized information propagation mechanism in networks we call the coalescing-branching random walk (cobra walk, for short). A cobra walk is a generalization of the well-studied "standard" random walk, and is useful in modeling and understanding the Susceptible-Infected Susceptible (SIS)-type of epidemic processes in networks. It can also be helpful in performing light-weight information dissemination in resource-constrained networks. A cobra walk is parameterized by a branching factor k. The process starts from an arbitrary node, which is labeled active for step 1. (For instance, this could be a node that has a piece of data, rumor, or a virus.) In each step of a cobra walk, each active node chooses k random neighbors to become active for the next step ("branching"). A node is active for step t + 1 only if it is chosen by an active node in step t ("coalescing"). This results in a stochastic process in the underlying network with properties that are quite different from both the standard random walk (which is equivalent to the cobra walk with branching factor 1) as well as other gossip-based rumor spreading mechanisms. We focus on the cover time of the cobra walk, which is the number of steps for the walk to reach all the nodes, and derive almost-tight bounds for various graph classes. Our main technical result is an O(log2 n) high probability bound for the cover time of cobra walks on expanders, if either the expansion factor or the branching factor is sufficiently large; we also obtain an O(log n) high probability bound for the partial cover time, which is the number of steps needed for the walk to reach at least a constant fraction of the nodes. We show that the cobra walk takes O(n log n) steps on any n-node tree for k ≥ 2, and Õ(n1/d) steps on a d-dimensional grid for k ≥ 2, with high probability.