Analyzing Kleinberg's (and other) small-world Models

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Analyzing Kleinberg's (and other) small-world Models
We analyze the properties of Small-World networks, where links are much more likely to connect “neighbor nodes” than distant nodes. In particular, our analysis provides new results for Kleinberg’s Small-World model and its extensions. Kleinberg adds a number of directed long-range random links to an n×n lattice network (vertices as nodes of a grid, undirected edges between any two adjacent nodes). Links have a non-uniform distribution that favors arcs to close nodes over more distant ones. He shows that the following phenomenon occurs: between any two nodes a path with expected length O(log2 n) can be found using a simple greedy algorithm which has no global knowledge of long-range links. We show that Kleinberg’s analysis is tight: his algorithm achieves θ(log2 n) delivery time. Moreover, we show that the expected diameter of the graph is θ(log n), a log n factor smaller. We also extend our results to the general kdimensional model. Our diameter results extend traditional w...
Charles U. Martel, Van Nguyen
Added 30 Jun 2010
Updated 30 Jun 2010
Type Conference
Year 2004
Where PODC
Authors Charles U. Martel, Van Nguyen
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