# Decomposable Submodular Function Minimization via Maximum Flow

@inproceedings{Axiotis2021DecomposableSF, title={Decomposable Submodular Function Minimization via Maximum Flow}, author={Kyriakos Axiotis and Adam Karczmarz and A. Mukherjee and Piotr Sankowski and Adrian Vladu}, booktitle={ICML}, year={2021} }

This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times for this problem by reducing it to a number of calls to a maximum flow oracle. When each function in the decomposition acts on O(1) elements of the ground set V and is polynomially bounded, our running time is up to polylogarithmic factors equal to that of solving maximum flow in a sparse graph with…

## 4 Citations

### Approximate Decomposable Submodular Function Minimization for Cardinality-Based Components

- Computer ScienceNeurIPS
- 2021

This work develops the first approximation algorithms for this problem, where the approximations can be quickly computed via reduction to a sparse graph cut problem, with graph sparsity controlled by the desired approximation factor.

### Decomposable Non-Smooth Convex Optimization with Nearly-Linear Gradient Oracle Complexity

- Computer Science, MathematicsArXiv
- 2022

This work gives an algorithm that minimizes the above convex formulation to ǫ -accuracy in e O ( P ni =1 d i log(1 /ǫ )) gradient computations, with no assumptions on the condition number.

### Augmented Sparsifiers for Generalized Hypergraph Cuts with Applications to Decomposable Submodular Function Minimization

- Computer Science
- 2020

A new framework of sparsifying hypergraph-to-graph reductions is introduced, where a hypergraph cut defined by submodular cardinality-based splitting functions is (1+ε)-approximated by a cut on a directed graph.

### Sparsification of Decomposable Submodular Functions

- Computer Science, MathematicsAAAI
- 2022

This work introduces the notion of sparsification for decomposable sub modular functions whose objective is to obtain an accurate approximation of the original function that is a (weighted) sum of only a few submodular functions.

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