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]

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 and multigraph matching 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

or

python3 -m pip install git+https://github.com/lpmp/LPMP.git@keypiont_submission

for the precise version used in [8].

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.

• [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.