Matching is as easy as matrix inversion
Combinatorica
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
The weighted majority algorithm
Information and Computation
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Polylog-time and near-linear work approximation scheme for undirected shortest paths
Journal of the ACM (JACM)
Network Flows and Matching: First DIMACS Implementation Challenge
Network Flows and Matching: First DIMACS Implementation Challenge
ACM SIGGRAPH 2003 Papers
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Are loss functions all the same?
Neural Computation
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Second-order Cone Programming Methods for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
Journal of Mathematical Imaging and Vision
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
A linear work, O(n1/6) time, parallel algorithm for solving planar Laplacians
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Faster approximate lossy generalized flow via interior point algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Approaching Optimality for Solving SDD Linear Systems
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Near linear-work parallel SDD solvers, low-diameter decomposition, and low-stretch subgraphs
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs
Proceedings of the forty-third annual ACM symposium on Theory of computing
A Nearly-m log n Time Solver for SDD Linear Systems
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Faster approximate multicommodity flow using quadratically coupled flows
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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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 connection demonstrates the difficulties of obtaining runtime guarantees, it also suggests an approach of using techniques originally developed for graph algorithms. We then show that most of these problems can be formulated as a grouped least squares problem, and give efficient algorithms for this formulation. Our algorithms rely on routines for solving quadratic minimization problems, which in turn are equivalent to solving linear systems. Some preliminary experimental work on image processing tasks are also presented.