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Resource discovery in distributed networks
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Deterministic resource discovery in distributed networks
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Spatial gossip and resource location protocols
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Protocols and Impossibility Results for Gossip-Based Communication Mechanisms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A stochastic process on the hypercube with applications to peer-to-peer networks
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Gossip-Based Computation of Aggregate Information
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The influence of search engines on preferential attachment
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
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The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
Computing separable functions via gossip
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Asynchronous resource discovery
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T-Man: Gossip-based fast overlay topology construction
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A distributed polylogarithmic time algorithm for self-stabilizing skip graphs
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Almost tight bounds for rumour spreading with conductance
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Optimal gossip-based aggregate computation
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Optimal cover time for a graph-based coupon collector process
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Semantic agent system for automatic mobilization of distributed and heterogeneous resources
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We study randomized gossip-based processes in dynamic networks that are motivated by information discovery in large-scale distributed networks such as peer-to-peer and social networks. A well-studied problem in peer-to-peer networks is resource discovery, where the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. Also, some of the recent work on self-stabilization algorithms for P2P/overlay networks proceed via discovery of the complete network. In social networks, nodes (people) discover new nodes through exchanging contacts with their neighbors (friends). In both cases the discovery of new nodes changes the underlying network --- new edges are added to the network --- and the process continues in the changed network. Rigorously analyzing such dynamic (stochastic) processes in a continuously changing topology remains a challenging problem with obvious applications. This paper studies and analyzes two natural gossip-based discovery processes. In the push discovery or triangulation process, each node repeatedly chooses two random neighbors and connects them (i.e., "pushes" their mutual information to each other). In the pull discovery process or the {\em two-hop walk}, each node repeatedly requests or "pulls" a random contact from a random neighbor and connects itself to this two-hop neighbor. Both processes are lightweight in the sense that the amortized work done per node is constant per round, local, and naturally robust due to the inherent randomized nature of gossip. Our main result is an almost-tight analysis of the time taken for these two randomized processes to converge. We show that in any undirected n-node graph both processes take O(n log2 n) rounds to connect every node to all other nodes with high probability, whereas Ω(n log n) is a lower bound. We also study the two-hop walk in directed graphs, and show that it takes O(n2 log n) time with high probability, and that the worst-case bound is tight for arbitrary directed graphs, whereas Ω(n2) is a lower bound for strongly connected directed graphs. A key technical challenge that we overcome in our work is the analysis of a randomized process that itself results in a constantly changing network leading to complicated dependencies in every round. We discuss implications of our results and their analysis to discovery problems in P2P networks as well as to evolution in social networks.