Combinatorica
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
The maximum concurrent flow problem
Journal of the ACM (JACM)
Fast approximation algorithms for fractional packing and covering problems
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Estimating the largest eigenvalues by the power and Lanczos algorithms with a random start
SIAM Journal on Matrix Analysis and Applications
Randomized algorithms
Approximating s-t minimum cuts in Õ(n2) time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Cut problems and their application to divide-and-conquer
Approximation algorithms for NP-hard problems
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Randomized rounding without solving the linear program
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
A linear time 2 + &&egr; approximation algorithm for edge connectivity
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
Approximation algorithms
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Convex Optimization
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth 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
Graph partitioning using single commodity flows
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On partitioning graphs via single commodity flows
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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This paper shows how to compute $O(\sqrt{\log n})$-approximations to the Sparsest Cut and Balanced Separator problems in $\tilde{O}(n^2)$ time, thus improving upon the recent algorithm of Arora, Rao, and Vazirani [Proceedings of the 36th Annual ACM Symposium on Theory of Computing, 2004, pp. 222-231]. Their algorithm uses semidefinite programming and requires $\tilde{O}(n^{9.5})$ time. Our algorithm relies on efficiently finding expander flows in the graph and does not solve semidefinite programs. The existence of expander flows was also established by Arora, Rao, and Vazirani [Proceedings of the 36th Annual ACM Symposium on Theory of Computing, 2004, pp. 222-231].