Corpus ID: 232134951

# Decomposable Submodular Function Minimization via Maximum Flow

@inproceedings{Axiotis2021DecomposableSF,
title={Decomposable Submodular Function Minimization via Maximum Flow},
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… Expand
1 Citations
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. Expand

#### References

SHOWING 1-10 OF 65 REFERENCES
Efficient Minimization of Decomposable Submodular Functions
• Computer Science, Mathematics
• NIPS
• 2010
This paper develops an algorithm, SLG, that can efficiently minimize decomposable submodular functions with tens of thousands of variables, and applies it to synthetic benchmarks and a joint classification-and-segmentation task, and shows that it outperforms the state-of-the-art general purpose sub modular minimization algorithms by several orders of magnitude. Expand
Minimizing a sum of submodular functions
• V. Kolmogorov
• Computer Science, Mathematics
• Discret. Appl. Math.
• 2012
This work casts the problem of minimizing a function represented as a sum of submodular terms in an auxiliary graph in such a way that applying most existing SF algorithms would rely only on these subroutines, and shows how to improve its complexity in the case when the function contains cardinality-dependent terms. Expand
Fast Decomposable Submodular Function Minimization using Constrained Total Variation
• Mathematics, Computer Science
• NeurIPS
• 2019
A modified convex problem requiring constrained version of the total variation oracles that can be solved with significantly fewer calls to the simple minimization oracles is considered. Expand
A fast algorithm for the generalized parametric minimum cut problem and applications
• Mathematics, Computer Science
• Algorithmica
• 2005
This paper shows how to remove both of these assumptions while obtaining the same running times as in Galloet al. Expand
On the Convergence Rate of Decomposable Submodular Function Minimization
• Computer Science, Mathematics
• NIPS
• 2014
It is shown that the algorithm converges linearly, and the upper and lower bounds on the rate of convergence are provided, which relies on the geometry of submodular polyhedra and draws on results from spectral graph theory. Expand
Geometric Rescaling Algorithms for Submodular Function Minimization
• Computer Science, Mathematics
• SODA
• 2018
A new class of polynomial-time algorithms for submodular function minimization (SFM), as well as a unified framework to obtain stronglyPolynomial SFM algorithms, which can be applied to a wide range of combinatorial and continuous algorithms, including pseudo-polynomial ones. Expand
A push-relabel framework for submodular function minimization and applications to parametric optimization
• Computer Science, Mathematics
• Discret. Appl. Math.
• 2003
This paper improves the running time of Schrijver's algorithm by designing a push-relabel framework for submodular function minimization (SFM), and extends this algorithm to carry out parametric minimization for a strong map sequence of sub modular functions in the same asymptotic running time as a single SFM. Expand
On the Approximation of Submodular Functions
• Computer Science, Mathematics
• ArXiv
• 2013
A large number of prior works imply that monotone submodular functions can be approximated by coverage functions with a factor between $O(\sqrt{n} \log n)$ and $\Omega(n^{1/3} /\log^2 n)$ and this work proves both upper and lower bounds on such approximations. Expand
A combinatorial strongly polynomial algorithm for minimizing submodular functions
• Mathematics, Computer Science
• JACM
• 2001
This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question posed in 1981 by Grötschel, Lovász, and Schrijver. The algorithm employsExpand