Perspectives of Monge properties in optimization
Discrete Applied Mathematics
A capacity scaling algorithm for convex cost submodular flows
Mathematical Programming: Series A and B
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Minimizing a submodular function arising from a concave function
Discrete Applied Mathematics
A fast cost scaling algorithm for submodular flow
Information Processing Letters
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Energy Minimization via Graph Cuts: Settling What is Possible
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
A faster strongly polynomial time algorithm for submodular function minimization
Mathematical Programming: Series A and B
A simple combinatorial algorithm for submodular function minimization
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Robust Higher Order Potentials for Enforcing Label Consistency
International Journal of Computer Vision
P³ & Beyond: Move Making Algorithms for Solving Higher Order Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Note: The expressive power of binary submodular functions
Discrete Applied Mathematics
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We consider the problem of minimizing a function represented as a sum of submodular terms. We assume each term allows an efficient computation of exchange capacities. This holds, for example, for terms depending on a small number of variables, or for certain cardinality-dependent terms. A naive application of submodular minimization algorithms would not exploit the existence of specialized exchange capacity subroutines for individual terms. To overcome this, we cast the problem as a submodular flow (SF) problem in an auxiliary graph in such a way that applying most existing SF algorithms would rely only on these subroutines. We then explore in more detail Iwata's capacity scaling approach for submodular flows (Iwata 1997 [19]). In particular, we show how to improve its complexity in the case when the function contains cardinality-dependent terms.