An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Lectures on Discrete Geometry
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Bounded Geometries, Fractals, and Low-Distortion Embeddings
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
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
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
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved lower bounds for embeddings into L1
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
Lp metrics on the Heisenberg group and the Goemans-Linial conjecture
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
How to Play Unique Games Using Embeddings
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A better approximation ratio for the vertex cover problem
ACM Transactions on Algorithms (TALG)
Coarse Differentiation and Multi-flows in Planar Graphs
Discrete & Computational Geometry
Breaking the Multicommodity Flow Barrier for O(vlog n)-Approximations to Sparsest Cut
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Bilipschitz snowflakes and metrics of negative type
Proceedings of the forty-second ACM symposium on Theory of computing
Sparsest cut on bounded treewidth graphs: algorithms and hardness results
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We exhibit an infinite doubling metric space (X,d) such that for any non-expansive f : X - L1, there exists a pair x,y ∈ X with d(x,y) arbitrarily large, and such that |f(x)-f(y)\|1/d(x,y) ≲ √log log d(x,y)}/(log d(x,y)). As a consequence, we show that there are n-point doubling metrics which require distortion Ω(√{log n/(log log n)}) into L1, matching the upper bound of [Gupta-Krauthgamer-Lee, FOCS'03] up to a factor of O(√log log n). The best previous lower bound for doubling spaces, due to [Cheeger-Kleiner-Naor, FOCS'09] was of the form (log n)δ for some small, unspecified value of δ 0. Furthermore, this gives a nearly optimal integrality gap for a weak version of the SDP for the general Sparsest Cut Problem. The weak SDP suffices for all known rounding algorithms, and the best previous gap was of the order (log n)1/4/(log log n) [Lee-Moharrami, STOC'10].