Triangulation and Embedding using Small Sets of Beacons

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Triangulation and Embedding using Small Sets of Beacons (2008)

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by Jon Kleinberg , Aleksandrs Slivkins , Tom Wexler

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96 - 11 self

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@MISC{Kleinberg08triangulationand,
    author = {Jon Kleinberg and Aleksandrs Slivkins and Tom Wexler},
    title = {Triangulation and Embedding using Small Sets of Beacons },
    year = {2008}
}

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Abstract

Concurrent with recent theoretical interest in the problem of metric embedding, a growing body of research in the networking community has studied the distance matrix defined by node-to-node latencies in the Internet, resulting in a number of recent approaches that approximately embed this distance matrix into low-dimensional Euclidean space. There is a fundamental distinction, however, between the theoretical approaches to the embedding problem and this recent Internet-related work: in addition to computational limitations, Internet measurement algorithms operate under the constraint that it is only feasible to measure distances for a linear (or near-linear) number of node pairs, and typically in a highly structured way. Indeed, the most common framework for Internet measurements of this type is a beacon-based approach: one chooses uniformly at random a constant number of nodes (‘beacons’) in the network, each node measures its distance to all beacons, and one then has access to only these measurements for the remainder of the algorithm. Moreover, beacon-based algorithms are often designed not for embedding but for the more basic problem of triangulation, in which one uses the triangle inequality to infer the distances that have not been measured. Here we give algorithms with provable performance guarantees for beacon-based triangulation and

Keyphrases

small set distance matrix constant number recent theoretical interest embedding problem provable performance guarantee node-to-node latency triangle inequality beacon-based triangulation low-dimensional euclidean space theoretical approach fundamental distinction metric embedding beacon-based algorithm recent internet-related work internet measurement algorithm operate recent approach node pair structured way basic problem computational limitation beacon-based approach internet measurement networking community common framework

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