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In this paper we show how to accelerate randomized coordinate descent methods and achieve faster convergence rates without paying per-iteration costs in asymptotic running time. In particular, we show how to generalize and efficiently implement a method proposed by Nesterov, giving faster asymptotic running times for various algorithms that use standard(More)
In this paper, we introduce a new framework for approximately solving flow problems in capacitated, undirected graphs and apply it to provide asymptotically faster algorithms for the maximum s-t flow and maximum concurrent multicommodity flow problems. For graphs with n vertices and m edges, it allows us to find an ε-approximate maximum s-t flow in time(More)
In this paper, we present a new algorithm for '/ solving linear programs that requires only Õ(√rank(A)L) iterations where A is the constraint matrix of a linear program with m constraints, n variables, and bit complexity L. Each iteration of our method consists of solving Õ(1) linear systems and additional nearly linear time(More)
In this paper we improve upon the running time for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set K &#x2282; R<sup>n</sup> that is contained in a box of radius R we show how to either compute a point in K or prove that K does not contain a ball of radius &#x03F5; using an expected O(n(More)
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time significantly. For theoretical performance guarantees, each row must be sampled with probability proportional to its(More)
We propose a new method for unconstrained optimization of a smooth and strongly convex function, which attains the optimal rate of convergence of Nesterov’s accelerated gradient descent. The new algorithm has a simple geometric interpretation, loosely inspired by the ellipsoid method. We provide some numerical evidence that the new method can be superior to(More)
We present the first single pass algorithm for computing spectral sparsifiers of graphs in the dynamic semi-streaming model. Given a single pass over a stream containing insertions and deletions of edges to a graph, G, our algorithm maintains a randomized linear sketch of the incidence matrix into dimension O(1/&#x2208;<sup>2n</sup>polylog(n)). Using this(More)
Let &#966;(G) be the minimum conductance of an undirected graph G, and let 0=&#955;<sub>1</sub> &#8804; &#955;<sub>2</sub> &#8804; ... &#8804; &#955;<sub>n</sub> &#8804; 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k &#8805; 2, [&#966;(G) = O(k) l<sub>2</sub>/&#8730;l<sub>k</sub>,] and this performance(More)
We give an algorithm which computes a (1-&#949;)-approximately maximum st-flow in an undirected uncapacitated graph in time O(1/&#949;&#8730;m/F&#8901; m log<sup>2</sup> n) where <i>F</i> is the flow value. By trading this off against the Karger-Levine algorithm for undirected graphs which takes ~O(m+nF) time, we obtain a running time of ~O(m(More)
In this paper we present an Õ(m √ n log U) time algorithm for solving the maximum flow problem on directed graphs with m edges, n vertices, and capacity ratio U . This improves upon the previous fastest running time of O(mmin ( n,m ) log ( n/m ) logU) achieved over 15 years ago by Goldberg and Rao [8] and improves upon the previous best running times for(More)