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

- 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)

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)

- 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)

- Aleksander Madry
- Inf. Process. Lett.
- 2005

- 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
- 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)

Recent work has demonstrated that neural networks are vulnerable to adversarial examples, i.e., inputs that are almost indistinguishable from natural data and yet classified incorrectly by the network. In fact, some of the latest findings suggest that the existence of adversarial attacks may be an inherent weakness of deep learning models. To address this… (More)

- Yossi Azar, Aleksander Madry, Thomas Moscibroda, Debmalya Panigrahi, Aravind Srinivasan
- Theor. Comput. Sci.
- 2009

Traditionally, network optimization problems assume that each link in the network has a fixed capacity. Recent research in wireless networking has shown that it is possible to design networks where the capacity of the links can be changed adaptively to suit the needs of specific applications. In particular, one gets a choice of having a few high capacity… (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)