Finding nearest neighbors in growth-restricted metrics

Karger, David R.; Ruhl, Matthias

doi:10.1145/509907.510013

Cited by 234 publications

(204 citation statements)

References 10 publications

(12 reference statements)

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“…The doubling dimension extends the notion of dimension from Euclidean spaces to arbitrary metric spaces. It has proven to be useful in many application domains such as nearest neighbor queries to databases [7], network construction [1], closest server selction [17], etc. Doubling metrics have notably been used to model distances in networks such as Internet [10].…”

Section: Related Workmentioning

confidence: 99%

Self-organizing flows in social networks

Hegde¹,

Massoulié

Viennot

2015

Theoretical Computer Science

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Social networks offer users new means of accessing information, essentially relying on "social filtering", i.e. propagation and filtering of information by social contacts. The sheer amount of data flowing in these networks, combined with the limited budget of attention of each user, makes it difficult to ensure that social filtering brings relevant content to interested users. Our motivation in this paper is to measure to what extent self-organization of a social network results in efficient social filtering.To this end we introduce flow games, a simple abstraction that models network formation under selfish dynamics, featuring user-specific * Part of this work was done while at Technicolor. † Supported by the Inria project-team "Gang" in the "LIAFA" laboratory and by the "LINCS" laboratory. 1interests and budget of attention. In the context of homogeneous user interests, we show that selfish dynamics converge to a stable network structure (namely a pure Nash equilibrium) with close-to-optimal information dissemination. We show that, in contrast, for the more realistic case of heterogeneous interests, selfish dynamics may lead to information dissemination that can be arbitrarily inefficient, as captured by an unbounded "price of anarchy".Nevertheless the situation differs when user interests exhibit a particular structure, captured by a metric space with low doubling dimension. In that case, natural autonomous dynamics converge to a stable configuration. Moreover, users obtain all the information of interest to them in the corresponding dissemination, provided their budget of attention is logarithmic in the size of their interest set.

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Section: Related Workmentioning

confidence: 99%

Self-organizing flows in social networks

Hegde¹,

Massoulié

Viennot

2015

Theoretical Computer Science

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“…≤ γk This is a similar restriction to the doubling metric restriction on metric spaces [10] and has been used before [15]. Throughout the analysis, we will assume that P has an expansion constant γ =O(1).…”

Section: Analysis Of the Algorithmmentioning

confidence: 99%

“…Given a point set of size n it uses only O(n) space. We show that with a bounded expansion constant γ (as described in [15]), using p threads (assuming p cores are available for computation) we can compute the k-NNG in O( n p k log k) unit steps, plus one parallel sort on the input. We also present extensive experimental results on a variety of architectures.…”

Section: Introductionmentioning

confidence: 99%

Fast construction of k-nearest neighbor graphs for point clouds

Connor

Kumar

2010

IEEE Trans. Visual. Comput. Graphics

124

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Abstract-We present a parallel algorithm for k-nearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: (1) Faster construction of k-nearest neighbor graphs in practice on multi-core machines. (2) Less space usage. (3) Better cache efficiency. (4) Ability to handle large data sets. (5) Ease of parallelization and implementation. If the point set has a bounded expansion constant, our algorithm requires one comparison based parallel sort of points according to Morton order plus near linear additional steps to output the k-nearest neighbor graph.

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“…There are several related definitions. Given a metric (P, τ ), let B(p, r) = {v | τ (p, v) ≤ r} denote the radius r ball centered at p. In [15], a metric has bounded expansion rate (also called the KR-dimension, counting measure)…”

Section: Preliminariesmentioning

confidence: 99%

Resilient and Low Stretch Routing through Embedding into Tree Metrics

Gao

Zhou

2011

Lecture Notes in Computer Science

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Abstract. Given a network, the simplest routing scheme is probably routing on a spanning tree. This method however does not provide good stretch -the route between two nodes can be much longer than their shortest distance, nor does it give good resilience -one node failure may disconnect quadratically many pairs. In this paper we use two trees to achieve both constant stretch and good resilience. Given a metric (e.g., as the shortest path metric of a given communication network), we build two hierarchical well-separated trees using randomization such that for any two nodes u, v, the shorter path of the two paths in the two respective trees gives a constant stretch of the metric distance of u, v, and the removal of any node only disconnect the routes between O(1/n) fraction of all pairs. Both bounds are in expectation and hold true as long as the metric follows certain geometric growth rate (the number of nodes within distance r is a polynomial function of r), which holds for many realistic network settings such as wireless ad hoc networks and Internet backbone graphs. The algorithms have been implemented and tested on real data.

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Finding nearest neighbors in growth-restricted metrics

Cited by 234 publications

References 10 publications

Self-organizing flows in social networks

Self-organizing flows in social networks

Fast construction of k-nearest neighbor graphs for point clouds

Resilient and Low Stretch Routing through Embedding into Tree Metrics

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