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
On the locality of bounded growth
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
On the establishment of distinct identities in overlay networks
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Meridian: a lightweight network location service without virtual coordinates
Proceedings of the 2005 conference on Applications, technologies, architectures, and protocols for computer communications
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
Energy conservation via domatic partitions
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Optimal-stretch name-independent compact routing in doubling metrics
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Using structure indices for efficient approximation of network properties
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
ACM SIGCOMM Computer Communication Review
Measurement based analysis, modeling, and synthesis of the internet delay space
Proceedings of the 6th ACM SIGCOMM conference on Internet measurement
On triangulation of simple networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Local embeddings of metric spaces
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Supporting network coordinates on PlanetLab
WORLDS'05 Proceedings of the 2nd conference on Real, Large Distributed Systems - Volume 2
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Reconstructing approximate tree metrics
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Compact routing with slack in low doubling dimension
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Towards fast decentralized construction of locality-aware overlay networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Embedding metrics into ultrametrics and graphs into spanning trees with constant average distortion
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Towards network triangle inequality violation aware distributed systems
Proceedings of the 7th ACM SIGCOMM conference on Internet measurement
Embedding metric spaces in their intrinsic dimension
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating TSP on metrics with bounded global growth
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Metric clustering via consistent labeling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A quicker way to discover nearby peers
CoNEXT '07 Proceedings of the 2007 ACM CoNEXT conference
Distributed algorithms for stable and secure network coordinates
Proceedings of the 8th ACM SIGCOMM conference on Internet measurement
On the internet delay space dimensionality
Proceedings of the 8th ACM SIGCOMM conference on Internet measurement
Using the doubling dimension to analyze the generalization of learning algorithms
Journal of Computer and System Sciences
Characteristics of Internet Latency and Their Impact on Distance Prediction Accuracy
CNSR '09 Proceedings of the 2009 Seventh Annual Communication Networks and Services Research Conference
Triangulation and embedding using small sets of beacons
Journal of the ACM (JACM)
Streaming Embeddings with Slack
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Fast shortest path distance estimation in large networks
Proceedings of the 18th ACM conference on Information and knowledge management
Practical connectivity-based routing in wireless sensor networks using dimension reduction
SECON'09 Proceedings of the 6th Annual IEEE communications society conference on Sensor, Mesh and Ad Hoc Communications and Networks
Labels, routing, and capacity: bringing theoretical networking closer to practice
INFOCOM'09 Proceedings of the 28th IEEE international conference on Computer Communications Workshops
Measurement-based analysis, modeling, and synthesis of the internet delay space
IEEE/ACM Transactions on Networking (TON)
VRAC: virtual raw anchor coordinate routing in sensor networks
WONS'10 Proceedings of the 7th international conference on Wireless on-demand network systems and services
Proximity algorithms for nearly-doubling spaces
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Virtual raw anchor coordinates: a new localization paradigm
ALGOSENSORS'10 Proceedings of the 6th international conference on Algorithms for sensor systems, wireless adhoc networks, and autonomous mobile entities
Distance distribution and average shortest path length estimation in real-world networks
ADMA'10 Proceedings of the 6th international conference on Advanced data mining and applications: Part I
A Lower Bound for Network Navigability
SIAM Journal on Discrete Mathematics
Querying shortest path distance with bounded errors in large graphs
SSDBM'11 Proceedings of the 23rd international conference on Scientific and statistical database management
Fast fully dynamic landmark-based estimation of shortest path distances in very large graphs
Proceedings of the 20th ACM international conference on Information and knowledge management
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Fast deterministic distributed maximal independent set computation on growth-bounded graphs
DISC'05 Proceedings of the 19th international conference on Distributed Computing
A highway-centric labeling approach for answering distance queries on large sparse graphs
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
Shortest-path queries for complex networks: exploiting low tree-width outside the core
Proceedings of the 15th International Conference on Extending Database Technology
Virtual raw anchor coordinates: A new localization paradigm
Theoretical Computer Science
Distributed and compact routing using spatial distributions in wireless sensor networks
ACM Transactions on Sensor Networks (TOSN)
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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 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 (ýbeaconsý) 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 驴 a certain fraction of all distances may be arbitrarily distorted. For metrics of bounded doubling dimension (which have been proposed as a reasonable abstraction of Internet latencies), we show that triangulation-based reconstruction with a constant number of beacons can achieve multiplicative error 1 + 驴 on a 1 - 驴 fraction of distances, for arbitrarily small constants 驴 and 驴. For this same class of metrics, we give a beacon-based embedding algorithm that achieves constant distortion on a 1- 驴 fraction of distances; this provides some theoretical justification for the success of the recent Global Network Positioning algorithm of Ng and Zhang, and it forms an interesting contrast with lower bounds showing that it is not possible to embed all distances in a doubling metric with constant distortion. We also give results for other classes of metrics, 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.