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Distance estimation and object location via rings of neighbors

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Abstract

We consider four problems on distance estimation and object location which share the common flavor of capturing global information via informative node labels: low-stretch routing schemes [48], distance labeling [25], searchable small worlds [31], and triangulation-based distance estimation [34]. Focusing on metrics of low doubling dimension, we approach these problems with a common technique called rings of neighbors, which refers to a sparse distributed data structure that underlies all our constructions. Apart from improving the previously known bounds for these problems, our contributions include extending Kleinberg’s small world model to doubling metrics, and a short proof of the main result in Chan et al. [15]. Doubling dimension is a notion of dimensionality for general metrics that has recently become a useful algorithmic concept in the theoretical computer science literature.

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Authors and Affiliations

  1. Department of Computer Science, Brown University, Providence, RI, 02912, USA

    Aleksandrs Slivkins

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Correspondence to Aleksandrs Slivkins.

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This work was done when A. Slivkins was a graduate student at Cornell University and was supported by the Packard Fellowship of Jon Kleinberg.

Preliminary version of this paper has appeared in 24th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC), 2005.

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Slivkins, A. Distance estimation and object location via rings of neighbors. Distrib. Comput. 19, 313–333 (2007). https://doi.org/10.1007/s00446-006-0015-8

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