Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete 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
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
Confronting hardness using a hybrid approach
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Optimal-stretch name-independent compact routing in doubling metrics
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
On space-stretch trade-offs: upper bounds
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
On triangulation of simple networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Labeling schemes for weighted dynamic trees
Information and Computation
Embedding metric spaces in their intrinsic dimension
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sdp gaps and ugc hardness for multiway cut, 0-extension, and metric labeling
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Dynamic routing schemes for graphs with low local density
ACM Transactions on Algorithms (TALG)
Triangulation and embedding using small sets of beacons
Journal of the ACM (JACM)
Volume in general metric spaces
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Hardness results for approximating the bandwidth
Journal of Computer and System Sciences
A Lower Bound for Network Navigability
SIAM Journal on Discrete Mathematics
Randomized compact routing in decomposable metrics
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Approximating the bandwidth of caterpillars
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
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We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability measure. This provides a refined and unified framework for the two primary methods of constructing Fr隆äechet embeddings for finite metrics, due to J. Bourgain and S. Rao. We prove that any n-point metric space (X, d) embeds in Hilbert space with distortion 0(\sqrt {\log \alpha \chi\cdot \log n}, where \alpha \chiis a geometric estimate on the decomposability of X. An an immediate corollary, we obtain an 0(\sqrt {\log \lambda \chi\cdot \log n} distortion embedding, where \lambda \chi is the doubling constant of X. Since \lambda \chi\leqslant n, this result recovers Bourgain's theorem, but when the metric X is, in a sense, "low-dimensional," improved bounds are achieved. Our embeddings are volume-respecting for subsets of arbitrary size. One consequence is the existence of (k, O(log n)) volume-respecting embeddings for all 1 \leqslant k \leqslant n, which is the best possible, and answers positively a question posed by U. Feige. Our techniques are also used to answer positively a question of Y. Rabinovich, showing that any weighted n-point planar graph embeds in \ell _\infty ^{0(\log n)} with O(1) distortion. The O(log n) bound on the dimension is optimal, and improves upon the previously known bound of O(log虏 n).