Locating nearby copies of replicated Internet servers
SIGCOMM '95 Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
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
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
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
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
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
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
Routing in Networks with Low Doubling Dimension
ICDCS '06 Proceedings of the 26th IEEE International Conference on Distributed Computing Systems
Algorithms on negatively curved spaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
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
Tapestry: a resilient global-scale overlay for service deployment
IEEE Journal on Selected Areas in Communications
Metric clustering via consistent labeling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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Network triangulation is a method for estimating distances betweennodes in the network, by letting every node measure its distanceto a few beacon nodes, and deducing the distance between every two nodes x,y by using their measurements to their common beaconsand applying the triangle inequality. Kleinberg, Slivkins and Wexler [FOCS 2004] initiated a theoretical study of triangulation in metric spaces, and Slivkins [PODC 2005] subsequently showed that metrics of bounded doubling dimension admit a triangulation thatapproximates arbitrarily well all pairwise distances using only O(log n) beacons per point, where n is the number of points in the network. He then asked whether this term is necessary (for doubling metrics). We provide the first lower bounds on the number of beacons required for a triangulation in some specific simple networks. In particular, these bounds (i) answer Slivkins' question positively, even for one-dimensional metrics, and (ii) prove that, up to constants, Slivkins' triangulation achieves an optimal number of beacons (as a function of the approximation guarantee and the doubling dimension).