The maximum concurrent flow problem
Journal of the ACM (JACM)
The weighted majority algorithm
Information and Computation
Las Vegas algorithms for linear and integer programming when the dimension is small
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Cut problems and their application to divide-and-conquer
Approximation algorithms for NP-hard problems
Semidefinite programming in combinatorial optimization
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Lectures on Discrete Geometry
Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On average distortion of embedding metrics into the line and into L1
Proceedings of the thirty-fifth 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
Cuts, Trees and ℓ1-Embeddings of Graphs*
Combinatorica
Expander flows, geometric embeddings and graph partitioning
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
On distance scales, embeddings, and efficient relaxations of the cut cone
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Euclidean distortion and the sparsest cut
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
On distance scales, embeddings, and efficient relaxations of the cut cone
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
An improved approximation ratio for the minimum linear arrangement problem
Information Processing Letters
Geometry, flows, and graph-partitioning algorithms
Communications of the ACM
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
Partitioning graphs into balanced components
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Expander flows, geometric embeddings and graph partitioning
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
Bilipschitz snowflakes and metrics of negative type
Proceedings of the forty-second ACM symposium on Theory of computing
Genus and the geometry of the cut graph
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
$O(\sqrt{\logn})$ Approximation to SPARSEST CUT in $\tilde{O}(n^2)$ Time
SIAM Journal on Computing
Near-optimal distortion bounds for embedding doubling spaces into L1
Proceedings of the forty-third annual ACM symposium on Theory of computing
Energy saving in fixed wireless broadband networks
INOC'11 Proceedings of the 5th international conference on Network optimization
Cut problems in graphs with a budget constraint
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Semidefinite programming and approximation algorithms: a survey
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
| Hi-index | 0.02 |
In this paper, we study the metrics of negative type, which are metrics (V, d) such that √d is an Euclidean metric; these metrics are thus also known as "l2-squared" metrics.We show how to embed n-point negative-type metrics into Euclidean space l2 with distortion D = O(log3/4 n). This embedding result, in turn, implies an O(log3/4 k)-approximation algorithm for the Sparsest Cut problem with non-uniform demands. Another corollary we obtain is that n-point subsets of l1 embed into l2 with distortion O(log3/4 n).