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A function $$f(x_1, \ldots , x_d)$$ f ( x 1 , … , x d ) , where each input is an integer from 1 to $$n$$ n and output is a real number, is Lipschitz if changing one of the inputs by 1 changes the output by at most 1. In other words, Lipschitz functions are not very sensitive to small changes in the input. Our main result is an efficient tester for the… (More)

- Natashia Boland, Santanu S Dey, Thomas Kalinowski, Marco Molinaro, Fabian Rigterink
- 2016

We investigate how well the graph of a bilinear function b : [0, 1] n → R can be approximated by its McCormick relaxation. In particular, we are interested in the smallest number c such that the difference between the concave upper bounding and convex lower bounding functions obtained from the McCormick relaxation approach is at most c times the difference… (More)

- Santanu S Dey, Marco Molinaro, Qianyi Wang
- 2016

In this paper, we present an analysis of the strength of sparse cutting-planes for mixed integer linear programs (MILP) with sparse formulations. We examine three kinds of problems: packing problems, covering problems, and more general MILPs with the only assumption that the objective function is non-negative. Given a MILP instance of one of these three… (More)

- Santanu S Dey, Marco Molinaro, Qianyi Wang
- 2015

In this paper, we present an analysis of the strength of sparse cutting-planes for mixed integer linear programs (MILP) with sparse formulations. We examine three kinds of problems: packing problems, covering problems, and more general MILPs with the only assumption that the objective function is non-negative. Given a MILP instance of one of these three… (More)

- Marco Molinaro, Gérard Cornuéjols, Dash Sanjeeb, Dey Santanu, Margot R François, Ravi
- 2013

Acknowledgements First and foremost, I must thank my advisor, Gérard Cornuéjols, for his unending support, advice, patience, flexibility and mentorship. I would also like to thank my committee members Sanjeeb Dash, Santanu Dey, François Margot and R. Ravi for their thoughtful comments and help throughout the dissertation process. I have been very fortunate… (More)

- Merve Bodur, Alberto Del, Pia, Santanu S Dey, Marco Molinaro, Sebastian Pokutta
- 2016

In this paper, we study the strength of Chvátal-Gomory (CG) cuts and more generally ag-gregation cuts for packing and covering integer programs (IPs). Aggregation cuts are obtained as follows: Given an IP formulation, we first generate a single implied inequality using aggre-gation of the original constraints, then obtain the integer hull of the set defined… (More)

- Research Showcase, Cmu, Negar Soheili Azad, Robert M Dean, Dammon, Zahra Afjeh +21 others
- 2015

The rapid growth in data availability has led to modern large scale convex optimization problems that pose new practical and theoretical challenges. Examples include classification problems such as customer segmentation in retail and credit scoring in insurance. Classical optimization and machine learning techniques are typically inadequate to solve these… (More)

- Negar Soheili Azad, Robert M Dean, Dammon, Zahra Afjeh, Ishani Aggarwal, Hamid Akhlaghi +19 others
- 2014

The rapid growth in data availability has led to modern large scale convex optimization problems that pose new practical and theoretical challenges. Examples include classification problems such as customer segmentation in retail and credit scoring in insurance. Classical optimization and machine learning techniques are typically inadequate to solve these… (More)

- Ravishankar Krishnaswamy, Nikhil Bansal, Avrim Blum, Anupam Gupta, Kirk Pruhs, R Ravi +12 others
- 2012

The views and conclusions contained in this document are those of the author and should not be interpreted as representing the ocial policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. Abstract The focus of this thesis is on the design and analysis of algorithms for basic problems in Stochastic… (More)

We study the following tree search problem: in a given tree T=(V,E) a vertex has been marked and we want to identify it. In order to locate the marked vertex, we can use edge queries. An edge query e asks in which of the two connected components of T∖e the marked vertex lies. The worst-case scenario where one is interested in minimizing the maximum number… (More)

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