On sparse spanners of weighted graphs
Discrete & Computational Geometry
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
Journal of the ACM (JACM)
Local versus global properties of metric spaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Reconstructing approximate tree metrics
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Local Global Tradeoffs in Metric Embeddings
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Using the last-mile model as a distributed scheme for available bandwidth prediction
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part I
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The theoretical computer science community has traditionally used embeddings of finite metrics as a tool in designing approximation algorithms. Recently, however, there has been considerable interest in using metric embeddings in the context of networks to allow network nodes to have more knowledge of the pairwise distances between other nodes in the network. There has also been evidence that natural network metrics like latency and bandwidth have some nice structure, and in particular come close to satisfying an 茂戮驴-three point condition or an 茂戮驴-four point condition. This empirical observation has motivated the study of these special metrics, including strong results about embeddings into trees and ultrametrics. Unfortunately all of the current embeddings require complete knowledge about the network up front, and so are less useful in real networks which change frequently. We give the first metric embeddings which have both low distortion and require only small changes in the structure of the embedding when the network changes. In particular, we give an embedding of semimetrics satisfying an 茂戮驴-three point condition into ultrametrics with distortion (1 + 茂戮驴)logn+ 4and the property that any new node requires only O(n1/3) amortized edge swaps, where we use the number of edge swaps as a measure of "structural change". This notion of structural change naturally leads to small update messages in a distributed implementation in which every node has a copy of the embedding. The natural offline embedding has only (1 + 茂戮驴)logndistortion but can require 茂戮驴(n) amortized edge swaps per node addition. This online embedding also leads to a natural dynamic algorithm that can handle node removals as well as insertions.