Bilipschitz snowflakes and metrics of negative type
Proceedings of the forty-second ACM symposium on Theory of computing
A general framework for graph sparsification
Proceedings of the forty-third annual ACM symposium on Theory of computing
Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
Near-optimal distortion bounds for embedding doubling spaces into L1
Proceedings of the forty-third annual ACM symposium on Theory of computing
Algorithmic extensions of cheeger's inequality to higher eigenvalues and partitions
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A fast solver for a class of linear systems
Communications of the ACM
Parallel graph decompositions using random shifts
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
A simple, combinatorial algorithm for solving SDD systems in nearly-linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
| Hi-index | 0.02 |
This paper ties the line of work on algorithms that find an O(√log(n))-approximation to the sparsest cut together with the line of work on algorithms that run in sub-quadratic time by using only single-commodity flows. We present an algorithm that simultaneously achieves both goals, finding an O(√log(n)/epsilon)-approximation using O(n^epsilon log^O(1) n) max-flows.The core of the algorithm is a stronger, algorithmic version of Arora et al.'s structure theorem, where we show that matching-chaining argument at the heart of their proof can be viewed as an algorithm that finds good augmenting paths in certain geometric multicommodity flow networks. By using that specialized algorithm in place of a black-box solver, we are able to solve those instances much more efficiently. We also show the cut-matching game framework can not achieve an approximation any better than Omega(log(n)/log log(n)) without re-routing flow.