Asymptotic theory of finite dimensional normed spaces
Asymptotic theory of finite dimensional normed spaces
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Lectures on Discrete Geometry
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Database-friendly random projections: Johnson-Lindenstrauss with binary coins
Journal of Computer and System Sciences - Special issu on PODS 2001
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
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
0(\sqrt {\log n)} Approximation to SPARSEST CUT in Õ(n2) Time
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On distance scales, embeddings, and efficient relaxations of the cut cone
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Metric structures in L1: dimension, snowflakes, and average distortion
European Journal of Combinatorics
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Directed metrics and directed graph partitioning problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Improved lower bounds for embeddings into L1
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Lattice problems and norm embeddings
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Hardness of cut problems in directed graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Volume distortion for subsets of Euclidean spaces: extended abstract
Proceedings of the twenty-second annual symposium on Computational geometry
The NP-completeness column: The many limits on approximation
ACM Transactions on Algorithms (TALG)
Cut problems in graphs with a budget constraint
Journal of Discrete Algorithms
Polynomial flow-cut gaps and hardness of directed cut problems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Vertex cuts, random walks, and dimension reduction in series-parallel graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An improved approximation ratio for the minimum linear arrangement problem
Information Processing Letters
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
ACM Transactions on Algorithms (TALG)
Optimal hierarchical decompositions for congestion minimization in networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Hardness of Embedding Metric Spaces of Equal Size
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Coarse Differentiation and Multi-flows in Planar Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Overcoming the l1 non-embeddability barrier: algorithms for product metrics
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Polynomial flow-cut gaps and hardness of directed cut problems
Journal of the ACM (JACM)
On the Optimality of Gluing over Scales
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Hard metrics from Cayley graphs of Abelian groups
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Local Global Tradeoffs in Metric Embeddings
SIAM Journal on Computing
Approximation algorithms and hardness of the k-route cut problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Cut problems in graphs with a budget constraint
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
A PRG for lipschitz functions of polynomials with applications to sparsest cut
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Hi-index | 0.00 |
We prove that every n-point metric space of negative type (in particular, every n-point subset of L1) embeds into a Euclidean space with distortion O(√log n log log n), a result which is tight up to the O(log log n) factor. As a consequence, we obtain the best known polynomial-time approximation algorithm for the Sparsest Cut problem with general demands. If the demand is supported on a subset of size k, we achieve an approximation ratio of O(√log k log log k).