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Distributed Object Location in a Dynamic Network
, 2004
"... Modern networking applications replicate data and services widely, leading to a need for locationindependent routingthe ability to route queries to objects using names independent of the objects' physical locations. Two important properties of such a routing infrastructure are routing locality a ..."
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Cited by 167 (16 self)
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Modern networking applications replicate data and services widely, leading to a need for locationindependent routingthe ability to route queries to objects using names independent of the objects' physical locations. Two important properties of such a routing infrastructure are routing locality and rapid adaptation to arriving and departing nodes. We show how these two properties can be efficiently achieved for certain network topologies. To do this, we present a new distributed algorithm that can solve the nearestneighbor problem for these networks. We describe our solution in the context of Tapestry, an overlay network infrastructure that employs techniques proposed by Plaxton et al. [24].
Meridian: A Lightweight Network Location Service without Virtual Coordinates
 In SIGCOMM
, 2005
"... This paper introduces a lightweight, scalable and accurate framework, called Meridian, for performing node selection based on network location. The framework consists of an overlay network structured around multiresolution rings, query routing with direct measurements, and gossip protocols for diss ..."
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Cited by 139 (7 self)
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This paper introduces a lightweight, scalable and accurate framework, called Meridian, for performing node selection based on network location. The framework consists of an overlay network structured around multiresolution rings, query routing with direct measurements, and gossip protocols for dissemination. We show how this framework can be used to address three commonly encountered problems, namely, closest node discovery, central leader election, and locating nodes that satisfy target latency constraints in largescale distributed systems without having to compute absolute coordinates. We show analytically that the framework is scalable with logarithmic convergence when Internet latencies are modeled as a growthconstrained metric, a lowdimensional Euclidean metric, or a metric of low doubling dimension. Large scale simulations, based on latency measurements from 6.25 million nodepairs as well as an implementation deployed on PlanetLab show that the framework is accurate and effective.
Bypassing the embedding: Algorithms for lowdimensional metrics
 In Proceedings of the 36th ACM Symposium on the Theory of Computing (STOC
, 2004
"... The doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2 k balls of radius r. This concept for abstract metrics has been proposed as a natural analog to the dimension of a Euclidean space. If we could embed metrics with low doubling dimension into l ..."
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Cited by 65 (4 self)
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The doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2 k balls of radius r. This concept for abstract metrics has been proposed as a natural analog to the dimension of a Euclidean space. If we could embed metrics with low doubling dimension into low dimensional Euclidean spaces, they would inherit several algorithmic and structural properties of the Euclidean spaces. Unfortunately however, such a restriction on dimension does not suffice to guarantee embeddibility in a normed space. In this paper we explore the option of bypassing the embedding. In particular we show the following for low dimensional metrics: • Quasipolynomial time (1+ɛ)approximation algorithm for various optimization problems such as TSP, kmedian and facility location. • (1 + ɛ)approximate distance labeling scheme with optimal label length. • (1+ɛ)stretch polylogarithmic storage routing scheme.
The blackbox complexity of nearest neighbor search
 In 31st International Colloquium on Automata, Languages and Programming
, 2004
"... We define a natural notion of efficiency for approximate nearestneighbor (ANN) search in general npoint metric spaces, namely the existence of a randomized algorithm which answers (1 + ε)approximate nearest neighbor queries in polylog(n) time using only polynomial space. We then study which famil ..."
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Cited by 29 (2 self)
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We define a natural notion of efficiency for approximate nearestneighbor (ANN) search in general npoint metric spaces, namely the existence of a randomized algorithm which answers (1 + ε)approximate nearest neighbor queries in polylog(n) time using only polynomial space. We then study which families of metric spaces admit efficient ANN schemes in the blackbox model, where only oracle access to the distance function is given, and any query consistent with the triangle inequality may be asked. For ε < 2 5, we offer a complete answer to this problem. Using the notion of metric dimension defined in [GKL03] (à la [Ass83]), we show that a metric space X admits an efficient (1+ε)ANN scheme for any ε < 2 5 if and only if dim(X) = O(log log n). For coarser approximations, clearly the upper bound continues to hold, but there is a threshold at which our lower bound breaks down—this is precisely when points in the “ambient space ” may begin to affect the complexity of “hard ” subspaces S ⊆ X. Indeed, we give examples which show that dim(X) does not characterize the blackbox complexity of ANN above the threshold. Our scheme for ANN in lowdimensional metric spaces is the first to yield efficient algorithms without relying on any additional assumptions on the input. In previous approaches (e.g., [Cla99, KR02, KL04, HKMR04]), even spaces with dim(X) = O(1) sometimes required Ω(n) query times. 1
Meridian: A Lightweight Framework for Network Location without Virtual Coordinates
 In Proc. of ACM SIGCOMM
, 2005
"... Selecting nodes based on their position in the network is a basic building block for many distributed systems. This paper describes a peertopeer overlay network for performing positionbased node selection. Our system, Meridian, provides a lightweight, accurate and scalable framework for keeping t ..."
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Cited by 1 (0 self)
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Selecting nodes based on their position in the network is a basic building block for many distributed systems. This paper describes a peertopeer overlay network for performing positionbased node selection. Our system, Meridian, provides a lightweight, accurate and scalable framework for keeping track of location information for participating nodes. The framework consists of an overlay network structured around multiresolution rings, query routing with direct measurements, and gossip protocols for dissemination. We show how this framework can be used to address three commonly encountered problems in largescale distributed systems without having to compute absolute coordinates; namely, closest node discovery, central leader election, and locating nodes that satisfy target latency constraints. We show analytically that the framework is scalable with logarithmic convergence when Internet latencies are modeled as a growthconstrained metric, a lowdimensional Euclidian metric, or a metric of low doubling dimension. Large scale simulations, based on latency measurements from 6.25 million nodepairs, and an implementation deployed on PlanetLab both show that the framework is accurate and effective. 1
Bypassing the Embedding: Approximation schemes andCompact Representations for Low Dimensional Metrics
"... ABSTRACT The doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2k balls of radius r. This concept for abstract metrics has been proposed as a natural analog to the dimension of a Euclidean space. If we could embed metrics with low doubling dimensio ..."
Abstract
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ABSTRACT The doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2k balls of radius r. This concept for abstract metrics has been proposed as a natural analog to the dimension of a Euclidean space. If we could embed metrics with low doubling dimension into low dimensional Euclidean spaces, they would inherit several algorithmic and structural properties of the Euclidean spaces. Unfortunately however, such a restriction on dimension does not suffice to guarantee embeddibility in a normed space. In this paper we explore the option of bypassing the embedding. In particular we show the following for low dimensional metrics: * Quasipolynomial time (1+ffl)approximation algorithm for various optimization problems such as TSP, kmedian and facility location. * (1 + ffl)approximate distance labeling scheme with optimal label length. * (1+ffl)stretch polylogarithmic storage routing scheme.
A Framework for Network LocationAware Node Selection
"... We introduce a lightweight, scalable and accurate framework for performing node selection based on network location. The framework, called Meridian, consists of an overlay network structured around multiresolution rings, gossip protocols for ring maintenance, and query routing with direct measureme ..."
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We introduce a lightweight, scalable and accurate framework for performing node selection based on network location. The framework, called Meridian, consists of an overlay network structured around multiresolution rings, gossip protocols for ring maintenance, and query routing with direct measurements to satisfy user specified latency constraints. We show how this framework can be used to address three commonly encountered problems, namely, closest node discovery, central leader election, and locating nodes that satisfy target latency constraints in largescale distributed systems without having to compute absolute coordinates. We also present the Meridian Query Language, a domain specific language for users to construct custom node selection queries based on their specific network location requirements. To facilitate adoption of Meridian, we have deployed a service called ClosestNode.com that provides a DNS to Meridian gateway for oblivious clients to initiate Meridian lookups. We show analytically that the framework is scalable with logarithmic convergence when Internet latencies are modeled as a growthconstrained metric, a lowdimensional Euclidean metric, or a metric of low doubling dimension. Large scale simulations, based on latency measurements from 6.25 million nodepairs as well as an implementation deployed on PlanetLab show that the framework is accurate and effective.