Abstract
Social networks support efficient decentralized search: people can collectively construct short paths to a specified target in the network. Rank-based friendship—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—is an empirically validated model of acquaintanceship that provably results in efficient decentralized search via greedy routing, even in networks with variable population densities. In this paper, we introduce cautious-greedy routing, a variant of greedy that avoids taking large jumps unless they make substantial progress towards the target. Our main result is that cautious-greedy routing finds a path of short expected length from an arbitrary source to a randomly chosen target, independent of the population densities. To quantify the expected length of the path, we define the depth of field of a metric space, a new quantity that intuitively measures the “width” of directions that leave a point in the space. Our main result is that cautious-greedy routing finds a path of expected length O(log2 n) in n-person networks that have aspect ratio polynomial in n, bounded doubling dimension, and bounded depth of field. Specifically, in k-dimensional grids under Manhattan distance with arbitrary population densities, the O(log2 n) expected path length that we achieve with the cautious-greedy algorithm improves the best previous bound of O(log3 n) with greedy routing.
Supported in part by grants from Carleton College and by NSF grant CCF-0728779. Thanks to Esteban Arcaute, Seth Gilbert, Ravi Kumar, Jeff Ondich, Andrew Tomkins, and Sergei Vassilvitskii for helpful conversations.
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Barbella, D., Kachergis, G., Liben-Nowell, D., Sallstrom, A., Sowell, B. (2007). Depth of Field and Cautious-Greedy Routing in Social Networks. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_50
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DOI: https://doi.org/10.1007/978-3-540-77120-3_50
Publisher Name: Springer, Berlin, Heidelberg
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