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14
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 148 (8 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.
Distance Estimation and Object Location via Rings of Neighbors
 In 24 th Annual ACM Symposium on Principles of Distributed Computing (PODC
, 2005
"... We consider four problems on distance estimation and object location which share the common flavor of capturing global information via informative node labels: lowstretch routing schemes [47], distance labeling [24], searchable small worlds [30], and triangulationbased distance estimation [33]. Fo ..."
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Cited by 66 (5 self)
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We consider four problems on distance estimation and object location which share the common flavor of capturing global information via informative node labels: lowstretch routing schemes [47], distance labeling [24], searchable small worlds [30], and triangulationbased distance estimation [33]. 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. [14]. Doubling dimension is a notion of dimensionality for general metrics that has recently become a useful algorithmic concept in the theoretical computer science literature. 1
Fast Deterministic Distributed Maximal Independent Set Computation on GrowthBounded Graphs
 In Proc. of the 19th International Symposium on Distributed Computing (DISC
, 2005
"... Abstract. The distributed complexity of computing a maximal independent set in a graph is of both practical and theoretical importance. While there exists an elegant O(log n) time randomized algorithm for general graphs [20], no deterministic polylogarithmic algorithm is known. In this paper, we st ..."
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Cited by 41 (11 self)
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Abstract. The distributed complexity of computing a maximal independent set in a graph is of both practical and theoretical importance. While there exists an elegant O(log n) time randomized algorithm for general graphs [20], no deterministic polylogarithmic algorithm is known. In this paper, we study the problem in graphs with bounded growth, an important family of graphs which includes the wellknown unit disk graph and many variants thereof. Particularly, we propose a deterministic algorithm that computes a maximal independent set in time O(log ∆ · log∗n) in graphs with bounded growth, where n and ∆ denote the number of nodes and the maximal degree in G, respectively. 1
Distributed Approaches to Triangulation and Embedding
, 2006
"... A number of recent papers in the networking community study the distance matrix defined by the nodetonode latencies in the Internet and, in particular, provide a number of quite successful distributed approaches that embed this distance into a lowdimensional Euclidean space. In such algorithms it ..."
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Cited by 30 (7 self)
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A number of recent papers in the networking community study the distance matrix defined by the nodetonode latencies in the Internet and, in particular, provide a number of quite successful distributed approaches that embed this distance into a lowdimensional Euclidean space. In such algorithms it is feasible to measure distances among only a linear or nearlinear number of node pairs; the rest of the distances are simply not available. Moreover, for applications it is desirable to spread the load evenly among the participating nodes. Indeed, several recent studies use this ’fully distributed ’ approach and achieve, empirically, a low distortion for all but a small fraction of node pairs. This is concurrent with the large body of theoretical work on metric embeddings, but there is a fundamental distinction: in the theoretical approaches to metric embeddings, full and centralized access to the distance matrix is assumed and heavily used. In this paper we present the first fully distributed embedding algorithm with provable distortion guarantees for doubling metrics (which have been proposed as a reasonable abstraction of Internet latencies), thus providing some insight into the empirical success of the recent Vivaldi algorithm [7]. The main ingredient of our embedding algorithm is an improved fully distributed algorithm for a more basic problem of triangulation, where the triangle inequality is used to infer the distances that have not been measured; this problem received a considerable attention in the networking community, and has also been studied theoretically in [19]. We use our techniques to extend ɛrelaxed embeddings and triangulations to infinite metrics and arbitrary measures, and to improve on the approximate distance labeling scheme of Talwar [36].
Compact Routing on Euclidian Metrics
, 2004
"... We consider the problem of designing a compact communication network that supports e#cient routing in an Euclidean plane. Our network design and routing scheme achieves 1+# stretch, logarithmic diameter, and constant out degree. This improves upon the best known result so far that requires a logari ..."
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Cited by 29 (4 self)
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We consider the problem of designing a compact communication network that supports e#cient routing in an Euclidean plane. Our network design and routing scheme achieves 1+# stretch, logarithmic diameter, and constant out degree. This improves upon the best known result so far that requires a logarithmic outdegree. Furthermore, our scheme is asymptotically optimal in Euclidean metrics whose diameter is polynomial.
Network Distance Estimation with Guarantees for All Node Pairs
, 2006
"... An active line of research in the networking community studies the distance matrix defined by the nodetonode latencies in the Internet and, in particular, provides a number of quite successful distributed approaches that approximately reconstruct these distances from observations. In such algorith ..."
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Cited by 3 (1 self)
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An active line of research in the networking community studies the distance matrix defined by the nodetonode latencies in the Internet and, in particular, provides a number of quite successful distributed approaches that approximately reconstruct these distances from observations. In such algorithms it is feasible to measure distances among only a linear or nearlinear number of node pairs; the rest of the distances are simply not available. The most common framework for Internet measurements of this type is a beaconbased approach: one chooses randomly 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. To obtain theoretical insight into these recent Internet measurement studies, Kleinberg et al. [17] formulated a concrete distance reconstruction problem, termed triangulation, where distances from a given node to beacons form a short node label, and the unobserved distances are inferred from these labels using triangle inequality. While several significant results have been obtained in this framework, all these results include a notion of slack: they provide no guarantees for a small fraction of node pairs. Essentially, for any given positive and δ, one can reconstruct all but an fraction of distances with multiplicative error at most 1 + δ, using only a constant number of beacons. In this paper we obtain triangulationstyle guarantees for all node pairs: we reconstruct all distances with multiplicative error at most 1 + δ, with only a polylogarithmic load on each participating node. Our guarantees are for growthconstrained metrics, a wellstudied family of metrics which have been proposed as a reasonable abstraction of Internet latencies. 1
Towards Fast Decentralized Construction of LocalityAware Overlay Networks
 In 26th Annual ACM SIGACTSIGOPS Symp. on Principles Of Distributed Computing (PODC
, 2007
"... We consider a large overlay network where any two nodes can communicate directly via the underlying Internet as long as the sender knows the recipient’s ipaddress. Due to the scalability requirement, the overlay network must be sparse: a given node can store at most a polylogarithmic number of ipad ..."
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Cited by 3 (0 self)
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We consider a large overlay network where any two nodes can communicate directly via the underlying Internet as long as the sender knows the recipient’s ipaddress. Due to the scalability requirement, the overlay network must be sparse: a given node can store at most a polylogarithmic number of ipaddresses. A notion of distance (locality) in the network is given by nodetonode roundtrip times. We assume that initially the overlay links are random, and hence have no explicit localityaware properties. We provide fast distributed constructions for various localityaware (lowstretch) distributed data structures, such as: distance labeling schemes, nameindependent routing schemes, and multicast trees. In previous work, such data structures have only been constructed via centralized algorithms. Our constructions complete in polylogarithmic time (and thus induce at most a polylogarithmic load on every given node), and achieve quality guarantees similar to those of the corresponding centralized algorithms. Our algorithms use a common localityaware, smallworldlike overlay framework, constructed via concurrent random walks. Our guarantees are for growthconstrained metrics, a wellstudied family of
EMBEDDING, DISTANCE ESTIMATION AND OBJECT LOCATION IN NETWORKS
, 2006
"... Concurrent with numerous theoretical results on metric embeddings, a growing body of research in the networking community has studied the distance matrix defined by nodetonode latencies in the Internet, resulting in a number of recent approaches that approximately embed this distance matrix into l ..."
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Cited by 2 (0 self)
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Concurrent with numerous theoretical results on metric embeddings, a growing body of research in the networking community has studied the distance matrix defined by nodetonode latencies in the Internet, resulting in a number of recent approaches that approximately embed this distance matrix into lowdimensional Euclidean space. A fundamental distinction between the theoretical approaches to embeddings and this recent Internetrelated work is that the latter operates under the additional constraint that it is only feasible to measure a linear number of node pairs, and typically in a highly structured way. Indeed, the most common framework here is a beaconbased approach: one randomly chooses a small number of nodes (’beacons’) in the network, and each node measures its distance to these beacons only. Moreover, beaconbased algorithms are also designed for the more basic problem of triangulation, in which one uses the triangle inequality to infer the distances that have not been measured. We give algorithms with provable performance guarantees for triangulation and embedding. We show that in addition to multiplicative error in the distances, performance guarantees for beaconbased algorithms typically must include a notion of ”slack ” – a certain fraction of all distances may be arbitrarily distorted. For arbitrary metrics, we give a beaconbased embedding algorithm that achieves constant distortion on a (1 − ɛ)fraction of distances; this provides some theoretical justification for the success of the recent
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