Methodologies and Algorithms for Group-Rankings Decision
Management Science
Optimal Real-Time Traffic Control in Metro Stations
Operations Research
Global optimization for first order Markov Random Fields with submodular priors
Discrete Applied Mathematics
Ranking sports teams and the inverse equal paths problem
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
An efficient and effective tool for image segmentation, total variations and regularization
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
New algorithms for convex cost tension problem with application to computer vision
Discrete Optimization
Hi-index | 0.00 |
We consider a convex, or nonlinear, separable minimization problem with constraints that are dual to the minimum cost network flow problem. We show how to reduce this problem to a polynomial number of minimum s,t-cut problems. The solution of the reduced problem utilizes the technique for solving integer programs on monotone inequalities in three variables, and a so-called proximity-scaling technique that reduces a convex problem to its linear objective counterpart. The problem is solved in this case in a logarithmic number of calls, O(log U), to a minimum cut procedure, where U is the range of the variables. For a convex problem on n variables the minimum cut is solved on a graph with O(n2) nodes. Among the consequences of this result is a new cut-based scaling algorithm for the minimum cost network flow problem. When the objective function is an arbitrary nonlinear function we demonstrate that this constrained problem is solved in pseudopolynomial time by applying a minimum cut procedure to a graph on O(nU) nodes.