A tight bound on approximating arbitrary metrics by tree metrics
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
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
On the Impossibility of Dimension Reduction in \ell _1
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Low dimensional embeddings of ultrametrics
European Journal of Combinatorics
Ordinal embeddings of minimum relaxation: general properties, trees, and ultrametrics
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Embedding ultrametrics into low-dimensional spaces
Proceedings of the twenty-second annual symposium on Computational geometry
Circular partitions with applications to visualization and embeddings
Proceedings of the twenty-fourth annual symposium on Computational geometry
Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics
ACM Transactions on Algorithms (TALG)
On low dimensional local embeddings
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Triangulation and embedding using small sets of beacons
Journal of the ACM (JACM)
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We prove that an ultrametric on n points can be embedded in ldp with distortion at most 1 + ε, and d = O(ε-2 log n). This bound matches the best known bound for the special case of an equilateral space.