Abstract
Social networks are navigable small worlds, in which two arbitrary people are likely connected by a short path of intermediate friends that can be found by a “decentralized” routing algorithm using only local information. We develop a model of social networks based on an arbitrary metric space of points, with population density varying across the points. We consider rank-based friendships, where the probability that person u befriends person v is inversely proportional to the number of people who are closer to u than v is. Our main result is that greedy routing can find a short path (of expected polylogarithmic length) from an arbitrary source to a randomly chosen target, independent of the population densities, as long as the doubling dimension of the metric space of locations is low. We also show that greedy routing finds short paths with good probability in tree-based metrics with varying population distributions.
Part of this work was done while the second author was visiting Yahoo! Research. Thanks to David Barbella, Erik Demaine, George Kachergis, David Karger, Jon Kleinberg, Danny Krizanc, Jasmine Novak, Prabhakar Raghavan, Anna Sallstrom, and Ben Sowell for helpful comments and suggestions.
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Kumar, R., Liben-Nowell, D., Tomkins, A. (2006). Navigating Low-Dimensional and Hierarchical Population Networks. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_44
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DOI: https://doi.org/10.1007/11841036_44
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