# Parallel Multicut Segmentation via Dual Decomposition

@inproceedings{Yarkony2014ParallelMS, title={Parallel Multicut Segmentation via Dual Decomposition}, author={Julian Yarkony and Thorsten Beier and Pierre Baldi and Fred A. Hamprecht}, booktitle={NFMCP}, year={2014} }

We propose a new outer relaxation of the multicut polytope, along with a dual decomposition approach for correlation clustering and multicut segmentation, for general graphs. Each subproblem is a minimum st-cut problem and can thus be solved efficiently. An optimal reparameterization is found using subgradients and affords a new characterization of the basic LP relaxation of the multicut problem, as well as informed decoding heuristics. The algorithm we propose for solving the problem…

## 7 Citations

### Massively Parallel Benders Decomposition for Correlation Clustering

- Computer ScienceArXiv
- 2019

The Benders decomposition approach provides a promising new avenue to accelerate optimization for CC, and allows for massive parallelization.

### A Benders Decomposition Approach to Correlation Clustering

- Computer Science2020 IEEE/ACM Workshop on Machine Learning in High Performance Computing Environments (MLHPC) and Workshop on Artificial Intelligence and Machine Learning for Scientific Applications (AI4S)
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The Benders decomposition approach provides a promising new avenue to accelerate optimization for CC, and, in contrast to previous cutting plane approaches, theoretically allows for massive parallelization.

### Planar Ultrametric Rounding for Image Segmentation

- Computer ScienceArXiv
- 2015

A dual cutting plane scheme is introduced that uses minimum cost perfect matching as a subroutine in order to efficiently explore the space of planar partitions and applies this algorithm to the problem of hierarchical image segmentation.

### Planar Ultrametrics for Image Segmentation

- Computer ScienceNIPS
- 2015

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of finding the closest ultrametric to a specified set of distances and solve it using an LP relaxation…

### A Message Passing Algorithm for the Minimum Cost Multicut Problem

- Computer Science2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
- 2017

An algorithm that alternates between message passing and efficient separation of cycle-and odd-wheel inequalities is defined, which is more efficient than state-of-the-art algorithms based on linear programming.

### Partial Optimality and Fast Lower Bounds for Weighted Correlation Clustering

- Computer ScienceICML
- 2018

A re-weighting with the dual solution by which efficient local search algorithms converge to better feasible solutions to solve the problem for series-parallel graphs to optimality, in linear time.

### Flow-Partitionable Signed Graphs

- Mathematics, Computer ScienceArXiv
- 2020

The class of flow-partitionable signed graphs is defined, which have the property that the standard linear programming relaxation based on so-called cycle inequalities is tight, and satisfy an exact max-multiflow-min-multicut relation in the associated instances of minimum multicut.

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