On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics)
SIAM Journal on Computing
Steiner points in tree metrics don't (really) help
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Constructing internet coordinate system based on delay measurement
Proceedings of the 3rd ACM SIGCOMM conference on Internet measurement
Virtual landmarks for the internet
Proceedings of the 3rd ACM SIGCOMM conference on Internet measurement
PIC: Practical Internet Coordinates for Distance Estimation
ICDCS '04 Proceedings of the 24th International Conference on Distributed Computing Systems (ICDCS'04)
Vivaldi: a decentralized network coordinate system
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
PCoord: Network Position Estimation Using Peer-to-Peer Measurements
NCA '04 Proceedings of the Network Computing and Applications, Third IEEE International Symposium
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
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Meridian: a lightweight network location service without virtual coordinates
Proceedings of the 2005 conference on Applications, technologies, architectures, and protocols for computer communications
Local versus global properties of metric spaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Algorithms on negatively curved spaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Operating system support for planetary-scale network services
NSDI'04 Proceedings of the 1st conference on Symposium on Networked Systems Design and Implementation - Volume 1
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
Proximity-preserving labeling schemes
Journal of Graph Theory
Distance labeling in hyperbolic graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Online and dynamic embeddings of approximate ultrametrics
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Online, Dynamic, and Distributed Embeddings of Approximate Ultrametrics
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
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
On the treeness of internet latency and bandwidth
Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems
Distributed relationship schemes for trees
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Greedy forwarding in dynamic scale-free networks embedded in hyperbolic metric spaces
INFOCOM'10 Proceedings of the 29th conference on Information communications
Brief announcement: decentralized network bandwidth prediction
DISC'10 Proceedings of the 24th international conference on Distributed computing
Local Global Tradeoffs in Metric Embeddings
SIAM Journal on Computing
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We introduce a novel measure called ε-four-pointscondition (ε-4PC), which assigns a value ε ∈ [0,1] to every metric space quantifying how close the metric is to a tree metric. Data-sets taken from real Internet measurements indicate remarkable closeness of Internet latencies to tree metrics based on this condition. We study embeddings of ε-4PC metric spaces into trees and prove tight upper and lower bounds. Specifically, we show that there are constants c1 and c2 such that, (1) every metric (X,d) which satisfies the ε-4PC can be embedded into a tree with distortion (1+ε)c1log|X|, and (2) for every ε ∈: [0,1] and any number of nodes, there is a metric space (X,d) satisfying the ε-4PC that does not embed into a tree with distortion less than (1+ε)c2log|X|. In addition, we prove a lower bound on approximate distance labelings of ε-4PC metrics, and give tight bounds for tree embeddings with additive error guarantees.