SIAM Journal on Applied Mathematics
Randomized algorithms
Locating nearby copies of replicated Internet servers
SIGCOMM '95 Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Accessing nearby copies of replicated objects in a distributed environment
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Sublinear time algorithms for metric space problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
IDMaps: a global internet host distance estimation service
IEEE/ACM Transactions on Networking (TON)
Finding nearest neighbors in growth-restricted metrics
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
King: estimating latency between arbitrary internet end hosts
Proceedings of the 2nd ACM SIGCOMM Workshop on Internet measurment
Property testing of data dimensionality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
The intrinsic dimensionality of graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On metric ramsey-type phenomena
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Finding Close Friends on the Internet
ICNP '01 Proceedings of the Ninth International Conference on Network Protocols
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Information and Computation
A note on the nearest neighbor in growth-restricted metrics
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Dimension reduction for ultrametrics
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Navigating nets: simple algorithms for proximity search
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Vivaldi: a decentralized network coordinate system
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
Measured Descent: A New Embedding Method for Finite Metrics
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Triangulation and Embedding Using Small Sets of Beacons
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Journal of Algorithms
Spatial gossip and resource location protocols
Journal of the ACM (JACM)
Fast construction of nets in low dimensional metrics, and their applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Distributed approaches to triangulation and embedding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Name independent routing for growth bounded networks
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Embedding, distance estimation and object location in networks
Embedding, distance estimation and object location in networks
Towards fast decentralized construction of locality-aware overlay networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
The geometry of graphs and some of its algorithmic applications
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Tapestry: a resilient global-scale overlay for service deployment
IEEE Journal on Selected Areas in Communications
Volume in general metric spaces
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Neighborhood-privacy protected shortest distance computing in cloud
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Indexing Network Structure with Shortest-Path Trees
ACM Transactions on Knowledge Discovery from Data (TKDD)
Partitioned multi-indexing: bringing order to social search
Proceedings of the 21st international conference on World Wide Web
Outsourcing shortest distance computing with privacy protection
The VLDB Journal — The International Journal on Very Large Data Bases
Efficient regression in metric spaces via approximate lipschitz extension
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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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 embedding. We show that in addition to multiplicative error in the distances, performance guarantees for beacon-based algorithms typically must include a notion of slack—a certain fraction of all distances may be arbitrarily distorted. For metric spaces of bounded doubling dimension (which have been proposed as a reasonable abstraction of Internet latencies), we show that triangulation-based distance reconstruction with a constant number of beacons can achieve multiplicative error 1 + δ on a 1 − ε fraction of distances, for arbitrarily small constants δ and ε. For this same class of metric spaces, we give a beacon-based embedding algorithm that achieves constant distortion on a 1 − ε fraction of distances; this provides some theoretical justification for the success of the recent Global Network Positioning algorithm of Ng and Zhang [2002], and it forms an interesting contrast with lower bounds showing that it is not possible to embed all distances in a doubling metric space with constant distortion. We also give results for other classes of metric spaces, as well as distributed algorithms that require only a sparse set of distances but do not place too much measurement load on any one node.