A Stochastic Process on the Hypercube with Applications to Peer-to-Peer Networks (2003) [34 citations — 1 self]

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by Micah Adler, Eran Halperin, Richard M. Karp, Vijay V. Vazirani

In Proceedings STOC

http://www.cc.gatech.edu/fac/Vijay.Vazirani/peer.ps

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@INPROCEEDINGS{Adler03astochastic,
    author = {Micah Adler and Eran Halperin and Richard M. Karp and Vijay V. Vazirani},
    title = {A Stochastic Process on the Hypercube with Applications to Peer-to-Peer Networks},
    booktitle = {In Proceedings STOC},
    year = {2003},
    pages = {575--584}
}

Abstract:

Consider the following stochastic process executed on a graph G = (V, E) whose nodes are initially uncovered. In each step, pick a node at random and if it is uncovered, cover it. Otherwise, if it has an uncovered neighbor, cover a random uncovered neighbor. Else, do nothing. This can be viewed as a structured coupon collector process. We show that for a large family of graphs, O(n) steps su#ce to cover all nodes of the graph with high probability, where n is the number of vertices. Among these graphs are d-regular graphs with d =#118 n log log n), random d-regular graphs with d =#906 n) and the k-dimensional hypercube where n = 2

Citations

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