# Fast Decomposable Submodular Function Minimization using Constrained Total Variation

arXiv: https://arxiv.org/abs/1905.11327 · HTML: https://mlsanity.com/paper/1905.11327/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2019.

## Built on by (most cited first, 1 of 1)

- [Decomposable Submodular Function Minimization via Maximum Flow](https://mlsanity.com/paper/2103.03868/) (2021)

## Abstract (arXiv)

We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding Lov'asz extensions and the squared Euclidean norm, leading to algorithms requiring total variation oracles of the summand functions; without further assumptions, these more complex oracles require many calls to the simpler minimization oracles often available in practice. In this paper, we consider 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. We support our claims by showing results on graph cuts for 2D and 3D graphs