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We consider integer programming problems $\max \{ c^T x : \mathcal{A} x = b, l \leq x \leq u, x \in \mathbb{Z}^{nt}\}$ where $\mathcal{A}$ has a (recursive) block-structure generalizing "$n$-fold integer programs" which recently received…
Optimizing the performance of stencil algorithms has been the subject of intense research over the last two decades. Since many stencil schemes have low arithmetic intensity, most optimizations focus on increasing the temporal data access…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…
This article introduces a highly parallel algorithm for molecular dynamics simulations with short-range forces on single node multi- and many-core systems. The algorithm is designed to achieve high parallel speedups for strongly…
The main focus of this paper is a pair of new approximation algorithms for certain integer programs. First, for covering integer programs {min cx: Ax >= b, 0 <= x <= d} where A has at most k nonzeroes per row, we give a k-approximation…
We study the multi-level Steiner tree problem: a generalization of the Steiner tree problem in graphs where terminals $T$ require varying priority, level, or quality of service. In this problem, we seek to find a minimum cost tree…
The Closest String Problem is an NP-hard problem that aims to find a string that has the minimum distance from all sequences that belong to the given set of strings. Its applications can be found in coding theory, computational biology, and…
One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel…
We consider the problem of selecting the best subset of exactly $k$ columns from an $m \times n$ matrix $A$. We present and analyze a novel two-stage algorithm that runs in $O(\min\{mn^2,m^2n\})$ time and returns as output an $m \times k$…
A stochastic Forward-Backward algorithm with a constant step is studied. At each time step, this algorithm involves an independent copy of a couple of random maximal monotone operators. Defining a mean operator as a selection integral, the…
Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to realizations that are uncertain. Algorithms designed to address multistage stochastic linear…
Multi-time-scale stochastic approximation is an iterative algorithm for finding the fixed point of a set of $N$ coupled operators given their noisy samples. It has been observed that due to the coupling between the decision variables and…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…
As the gap between compute and I/O performance tends to grow, modern High-Performance Computing (HPC) architectures include a new resource type: an intermediate persistent fast memory layer, called burst buffers. This is just one of many…
We study integer linear programs (ILP) of the form $\min\{c^\top x\ \vert\ Ax=b,l\le x\le u,x\in\mathbb Z^n\}$ and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the…
In this paper, we consider multi-stage stochastic optimization problems with convex objectives and conic constraints at each stage. We present a new stochastic first-order method, namely the dynamic stochastic approximation (DSA) algorithm,…
A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random and time varying topologies under unreliable and bandwidth-constrained communication network. This paper studies a stochastic…
In this paper, we design, analyze, and implement a variant of the two-loop L-shaped algorithms for solving two-stage stochastic programming problems that arise from important application areas including revenue management and power systems.…