LPMP is a C++ framework for developing scalable dual (Lagrangean) decomposition based solvers for a wide range of LP-relaxations to discrete optimization problems. For a theoretical introduction to the techniques used and the class of problems that can be optimized see [1,2].
We provide a range of solvers for various discrete optimization problems, including
- Discrete graphical models,
- Multicut, [3]
- Max-cut,
- Graph matching, [4]
- Multi-graph matching, [5]
- Discrete graphical models with bottleneck terms, [6]
- Lifted disjoint paths.
Benchmark problems for various solvers above can be found in datasets.
Optimization techniques include
- Messsage passing [1],
- Subgradient ascent with a proximal bundle method based on the Frank-Wolfe algorithm [2], Vladimir Kolmogorov's original implementation.
- An interface to external solvers is provided by DD_ILP.
The solvers can be wrapped as differentiable PyTorch modules using the technique of [7]. Currently, wrappers are available for graph matching, multigraph matching and lifted disjoint paths solvers. For usage examples see an application to keypoint matching [8] (code) or the general repository of [7].
All these can be pip installed with
python3 -m pip install git+https://github.com/LPMP/LPMP.git
In order to install only graph matching and multigraph matching solvers, type
PACKAGES="gm" python3 -m pip install git+https://github.com/LPMP/LPMP.git
In order to install only the lifted disjoint paths solver, type
PACKAGES="ldp" python3 -m pip install git+https://github.com/LPMP/LPMP.git
In order to install only the all variants of multicut solvers (multicut, asymmetric multiway cut [9], multiway cut [9]), type
PACKAGES="mc" python3 -m pip install git+https://github.com/LPMP/LPMP.git
In order to get the precise version of graph matching as used in [8], type
python3 -m pip install git+https://github.com/lpmp/LPMP.git@keypiont_submission
NOTE:
If you already installed with one of the above options and would like to change the option or if you have an older version installed, you must add --upgrade argument to pip. So, you type for instance
PACKAGES="ldp" python3 -m pip install git+https://github.com/lpmp/LPMP.git --upgrade
Type git clone https://github.com/LPMP/LPMP.git for downloading, then cd LPMP and git submodule update --init --remote --recursive for downloading dependencies and finally cmake . for building.
Prerequisites:
- Clang 5.0 or GCC 8.0 upwards for C++17 compatibility (see here for installation instructions).
- HDF5 (install with
apt install libhdf5-serial-dev) - cmake (install with
apt install cmake)
A tutorial on writing a new solver from scratch can be found here. The documentation for using all the existing solvers is in the directory doc.
- [1]:
P. Swoboda, J. Kuske and B. Savchynskyy. A Dual Ascent Framework for Lagrangean Decomposition of Combinatorial Problems. In CVPR 2017. - [2]:
P. Swoboda and V. Kolmogorov. MAP inference via Block-Coordinate Frank-Wolfe Algorithm. In CVPR 2019 - [3]:
P. Swoboda and B. Andres. A Message Passing Algorithm for the Minimum Cost Multicut Problem. In CVPR 2017. - [4]:
P. Swoboda, C. Rother, H. A. Alhaija, D. Kainmuller, B. Savchynskyy. A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching. In CVPR 2017. - [5]:
P. Swoboda, D. Kainmueller, A. Mokarian, C. Theobalt and F. Bernard. A convex approach to multi-graph matching. In CVPR 2019. - [6]:
A. Abbas, P. Swoboda. Bottleneck Potentials in Markov Random Fields. In ICCV 2019. - [7]:
M. Vlastelica, A. Paulus, V. Musil, G. Martius, M. Rolínek. Differentiation of Blackbox Combinatorial Solvers. In ICLR 2020. - [8]:
M. Rolínek, P. Swoboda, D. Zietlow, A. Paulus, V. Musil, G. Martius. Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers. - [9]:
A. Abbas, P. Swoboda. Combinatorial Optimization for Panoptic Segmentation: An End-to-End Trainable Approach.