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We consider the Asymmetric Traveling Salesman problem for costs satisfying the triangle inequality. We derive a ran-domized algorithm which delivers a solution within a factor O(log n/ log log n) of the optimum with high probability.

- Aleksander Madry
- 2013 IEEE 54th Annual Symposium on Foundations of…
- 2013

We present an Õ(m<sup>10/7</sup>) = Õ(m<sup>1.43</sup>)-time<sup>1</sup> algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities. This is the first improvement over the sparse-graph case of the long-standing O(m min{√m, n<sup>2/3</sup>}) running time bound due to Even and Tarjan… (More)

- Aleksander Madry
- 2010 IEEE 51st Annual Symposium on Foundations of…
- 2010

We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees, allows approximating it almost as quickly on general graphs while only losing a poly-logarithmic factor in the… (More)

- Katarzyna E. Paluch, Marcin Mucha, Aleksander Madry
- APPROX-RANDOM
- 2009

In the maximum traveling salesman problem (Max TSP) we are given a complete undirected graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. We present a fast combinatorial 4 5-approximation algorithm for Max TSP. The previous best approximation for this problem was 7 9. The new algorithm is based on… (More)

We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a system of linear equations in a Laplacian matrix, and thus may be approximately computed in nearly-linear time. Using this… (More)

- Jonathan A. Kelner, Aleksander Madry
- 2009 50th Annual IEEE Symposium on Foundations of…
- 2009

In this paper, we set forth a new algorithm for generating approximately uniformly random spanning trees in undirected graphs. We show how to sample from a distribution that is within a multiplicative $(1+\delta)$ of uniform in expected time $\TO(m\sqrt{n}\log 1/\delta)$. This improves the sparse graph case of the best previously known worst-case bound of… (More)

- Aleksander Madry
- STOC
- 2010

We combine the work of Garg and Konemann, and Fleischer with ideas from dynamic graph algorithms to obtain faster (1-ε)-approximation schemes for various versions of the multicommodity flow problem. In particular, if ε is moderately small and the size of every number used in the input instance is polynomially bounded, the running times of our… (More)

- Hui Han Chin, Aleksander Madry, Gary L. Miller, Richard Peng
- ITCS
- 2013

We study theoretical runtime guarantees for a class of optimization problems that occur in a wide variety of inference problems. These problems are motivated by the LASSO framework and have applications in machine learning and computer vision. Our work shows a close connection between these problems and core questions in algorithmic graph theory. While this… (More)

- Marcin Bienkowski, Aleksander Madry
- LATIN
- 2008

We study packet buffering, a basic problem occurring in network switches. We construct an optimal 16/13-competitive randomized online algorithm PB for the case of two input buffers of arbitrary sizes. Our proof is based on geometrical transformations which allow to identify the set of sequences incurring extremal competitive ratios. Later we may analyze the… (More)

- Nikhil Bansal, Niv Buchbinder, Aleksander Madry, Joseph Naor
- 2011 IEEE 52nd Annual Symposium on Foundations of…
- 2011

We give the first polylogarithmic-competitive randomized online algorithm for the <i>k</i>-server problem on an arbitrary finite metric space. In particular, our algorithm achieves a competitive ratio of Õ(log<sup>3</sup> <i>n</i> log<sup>2</sup> <i>k</i>) for any metric space on <i>n</i> points. Our algorithm improves upon the deterministic… (More)