Sparse Recovery With Integrality Constraints

On k-Column Sparse Packing Programs

We consider the class of packing integer programs (PIPs) that are column sparse, where there is a specified upper bound k on the number of constraints that each variable appears in. We give an improved (ek + o(k))-approximation algorithm for k-column sparse PIPs. Our algorithm is based on a linear programming relaxation, and involves randomized rounding combined with alteration. We also show th...

Iterative Packing for Demand and Hypergraph Matching

Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems, no single method has emerged that matches the effectiveness and simplicity afforded by the covering case. We offer a simple iterative packing technique that ...

Algorithms to Approximate Column-Sparse Packing Problems

Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation algorithms for some well-known families of such problems. As three main examples, we attain the integrality gap, up to lower-order terms, for known LP relaxat...

Total Dual Integrality of Matching Forest Constraints

Sparse Image and Video Recovery Using Gradient Projection for Linearly Constrained Convex Optimization

OF THE CAPSTONE PROJECT Sparse Image and Video Recovery Using Gradient Projection for Linearly Constrained Convex Optimization by Daniel Thompson May 2011 University of California, Merced Abstract This project concerns the reconstruction of a signal, which corresponds to either an image or a temporally-varying scene. Signal recovery can be accomplished through finding a sparse solution to an `2...