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Solving LPs with convergent message passing

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- README.md
- Advanced-Functions.md
- CMakeLists.txt
- Discrete-Tomography.md
- Getting-Started.md
- Graph-Matching.md
- Lifted-Disjoint-Paths.md
- Max-Cut.md
- MRF.md
- Multi-Graph-Matching.md
- Multicut.md
- QPBO_example.cpp
- QPBO_example.h
- README.md
- andres-graph
- arboricity
- BCFW-Bundle
- cpp-taskflow
- cudd
- DD_ILP
- Eigen
- LifT_Solver
- maxflow
- MCF-SSP
- meta
- opengm
- PEGTL
- pybind11
- qpbo
- TCLAP
- tsl-robin-map
- - asymmetric_multiway_cut_gaec.h
  - asymmetric_multiway_cut_instance.h
  - asymmetric_multiway_cut_parser.h
- - bdd_anisotropic_diffusion.h
  - bdd_branch_node.h
  - bdd_gradient_based_optimization.hxx
  - bdd_min_marginal_averaging.h
  - bdd_min_marginal_averaging_restricted.h
  - bdd_min_marginal_averaging_smoothed.h
  - bdd_primal_fixing.h
  - bdd_solver_interface.h
  - bdd_storage.h
  - bdd_variable.h
  - convert_pb_to_bdd.h
  - ILP_input.h
  - ILP_parser.h
- - cell_tracking_input.h
- - cut_base_apply_packing.hxx
  - cut_base_constructor.hxx
  - cut_base_instance.hxx
  - cut_base_lifted_constructor.hxx
  - cut_base_packing.h
  - cut_base_quadruplet_constructor.hxx
  - cut_base_quintuplet_constructor.hxx
  - cut_base_text_input.hxx
  - cut_base_triplet_constructor.hxx
  - lifted_factor.h
  - lifted_factor_messages.h
  - lifted_factors_messages.hxx
- - discrete_tomography_input.h
  - discrete_tomography_instance.h
- - LPMP_evaluate_log.py
- - labeling_list_factor.hxx
- - equality_message.hxx
  - graph_matching.h
  - graph_matching_constructor.hxx
  - graph_matching_frank_wolfe.h
  - graph_matching_frank_wolfe_impl.hxx
  - graph_matching_input.h
  - graph_matching_instance.h
  - graph_matching_instance_koopmans_beckmann.h
  - graph_matching_inter_quadratic_message.hxx
  - graph_matching_koopmans_beckmann_input.h
  - graph_matching_local_problem.hxx
  - graph_matching_python_binding_helper.h
  - matching_problem_input.h
  - min_cost_flow_factor_ssp.hxx
  - transform_matching_problem_input.hxx
- - horizon_tracking.h
  - horizon_tracking_chain_constructor.hxx
  - horizon_tracking_factors.hxx
  - horizon_tracking_MST_solver.hxx
  - horizon_tracking_primal_rounding.hxx
  - horizon_tracking_uai_input.h
  - horizon_tracking_util.hxx
  - spanning_trees.hxx
- - ldp_batch_process.hxx
  - ldp_complete_structure.hxx
  - ldp_cut_factor.hxx
  - ldp_cut_factor_separator.hxx
  - ldp_cut_message_creator.hxx
  - ldp_directed_graph.hxx
  - ldp_factor_queue.hxx
  - ldp_file_processing_methods.hxx
  - ldp_functions.hxx
  - ldp_gaec.hxx
  - ldp_instance.hxx
  - ldp_interval_connection.hxx
  - ldp_methods.hxx
  - ldp_min_marginals_extractor.hxx
  - ldp_parameter_parser.hxx
  - ldp_parameters.hxx
  - ldp_path_factor.hxx
  - ldp_path_separator.hxx
  - ldp_paths_extractor.hxx
  - ldp_primal_heuristics.hxx
  - ldp_single_node_cut.hxx
  - ldp_special_min_marginals_extractor.hxx
  - ldp_triangle_factor.hxx
  - ldp_two_layer_graph.hxx
  - ldp_vertex_groups.hxx
  - lifted_disjoint_paths_constructor.hxx
  - lifted_disjoint_paths_fmc.h
- - max_cut.h
  - max_cut_cycle_packing.h
  - max_cut_factors_messages.h
  - max_cut_greedy_additive_edge_contraction.h
  - max_cut_instance.hxx
  - max_cut_local_search.h
  - max_cut_odd_bicycle_wheel_packing.h
  - max_cut_quintuplet_constructor.hxx
  - max_cut_sahni_gonzalez.h
  - max_cut_text_input.h
  - max_cut_triplet_constructor.hxx
  - transform_binary_MRF.hxx
- - at_most_one_factor.h
  - binary_MRF_instance.hxx
  - cycle_inequalities.hxx
  - dimacs_max_flow_input.h
  - graphical_model.h
  - max_flow_instance.hxx
  - maxflow_factor.hxx
  - mrf_input.h
  - mrf_opengm_input.h
  - mrf_problem_construction.hxx
  - mrf_uai_input.h
  - mrf_uai_input_impl.hxx
  - pairwise_Potts_factor.h
  - pairwise_simplex_factor.h
  - qpbo_factor.hxx
  - simplex_factor.hxx
  - simplex_marginalization_message.hxx
  - ternary_simplex_factor.h
  - transform_max_flow_instance.hxx
  - unary_simplex_factor.h
- - andres_graph_utility.hxx
  - correlation_clustering_instance.h
  - multicut.h
  - multicut_andres_input.h
  - multicut_balanced_edge_contraction.h
  - multicut_constructor.hxx
  - multicut_cycle_packing.h
  - multicut_cycle_packing_parallel.h
  - multicut_factors.h
  - multicut_factors_messages.h
  - multicut_factors_messages.hxx
  - multicut_greedy_additive_edge_contraction.h
  - multicut_greedy_additive_edge_contraction_parallel.h
  - multicut_greedy_edge_fixation.h
  - multicut_instance.h
  - multicut_kernighan_lin.h
  - multicut_local_search.h
  - multicut_message_passing_parallel.h
  - multicut_odd_bicycle_wheel_packing.h
  - multicut_odd_wheel_packing.h
  - multicut_opengm_input.h
  - multicut_quadruplet_constructor.hxx
  - multicut_quintuplet_constructor.hxx
  - multicut_sequential_edge_fixation.hxx
  - multicut_text_input.h
  - multicut_triplet_constructor.hxx
  - transform_multigraph_matching.h
- - multigraph_matching.hxx
  - multigraph_matching_consistency_constraint.hxx
  - multigraph_matching_constructor.hxx
  - multigraph_matching_input.h
  - multigraph_matching_instance.h
  - multigraph_matching_koopman_beckmans_instance.h
  - multigraph_matching_simplex_triplet_consistency_messages.h
  - multigraph_matching_synchronization.h
  - multigraph_matching_triplet_consistency_factor.h
- - multiway_cut_gaec.h
  - multiway_cut_instance.h
- - standard_visitor.hxx
- atomic_helper.h
- bfs_ordering.hxx
- bipartite_graph_helper.hxx
- commutation_matrix.h
- config.hxx
- cuthill-mckee.h
- dynamic_graph.hxx
- dynamic_graph_thread_safe.hxx
- factor_container_interface.h
- factors_messages.hxx
- factors_partition_storage.hxx
- factors_storage.hxx
- function_existence.hxx
- graph.hxx
- grid.hxx
- hash_helper.hxx
- help_functions.hxx
- LP.h
- LP_external_interface.hxx
- LP_FWMAP.hxx
- lp_reparametrization.hxx
- mem_use.c
- memory_allocator.hxx
- MemoryPool.h
- MemoryPool.tcc
- message_passing_schedule.hxx
- message_passing_weight_computation.hxx
- messages_storage.hxx
- minimum_degree_ordering.hxx
- pegtl_parse_rules.h
- permutation.hxx
- polynomial_functions.h
- pseudo_peripheral_node.hxx
- send_messages_residual.hxx
- sequence_compression.h
- serialization.hxx
- solver.hxx
- spinlock.hxx
- template_utilities.hxx
- test.h
- three_dimensional_variable_array.hxx
- topological_sort.hxx
- tree_decomposition.hxx
- two_dimensional_variable_array.hxx
- union_find.hxx
- vector.hxx
- - __init__.py
  - graph_matching.py
  - multigraph_matching.py
  - utils.py
- __init__.py
- raw_solvers.py
- - __init__.py
  - graph_matching.py
  - multigraph_matching.py
  - utils.py
- __init__.py
- raw_solvers.py
- __init__.py
- multicut.py
- raw_solvers.py
- utils.py
- - asymmetric_multiway_cut_gaec.cpp
  - asymmetric_multiway_cut_gaec_text_input.cpp
  - asymmetric_multiway_cut_instance.cpp
  - asymmetric_multiway_cut_parser.cpp
  - asymmetric_multiway_cut_python_binding.cpp
  - CMakeLists.txt
- - bdd_anisotropic_diffusion_text_input.cpp
  - bdd_min_marginal_averaging_restricted_text_input.cpp
  - bdd_min_marginal_averaging_smoothed_text_input.cpp
  - bdd_min_marginal_averaging_text_input.cpp
  - bdd_projected_subgradient_text_input.cpp
  - CMakeLists.txt
  - ILP_parser.cpp
- - cell_tracking_input.cpp
  - CMakeLists.txt
  - convert_cell_tracking_to_lp.cpp
- - CMakeLists.txt
  - cut_base_packing.cpp
  - lifted_factor.cpp
- - CMakeLists.txt
  - convert_discrete_tomography_to_lp.cpp
  - discrete_tomography_input.cpp
- - __init__.py
  - CMakeLists.txt
  - convert_qaplib_to_dd.py
  - convert_torresani_et_al_to_lp.cpp
  - generate_graph_matching_solvers.py
  - graph_matching_frank_wolfe.cpp
  - graph_matching_frank_wolfe_koopmans_beckmann.cpp
  - graph_matching_frank_wolfe_koopmans_beckmann_text_input.cpp
  - graph_matching_frank_wolfe_sparse_text_input.cpp
  - graph_matching_frank_wolfe_text_input.cpp
  - graph_matching_gm.cpp
  - graph_matching_gm_proximal_bundle.cpp
  - graph_matching_gm_tightening.cpp
  - graph_matching_hungarian_bp.cpp
  - graph_matching_hungarian_bp_tightening.cpp
  - graph_matching_input.cpp
  - graph_matching_instance.cpp
  - graph_matching_instance_koopmans_beckmann.cpp
  - graph_matching_inter_quadratic_message.hxx
  - graph_matching_koopmans_beckmann_input.cpp
  - graph_matching_mcf_proximal_bundle.cpp
  - graph_matching_mp.cpp
  - graph_matching_mp_inter_quadratic_message.cpp
  - graph_matching_mp_inter_quadratic_message_tightening.cpp
  - graph_matching_mp_tightening.cpp
  - graph_matching_python_binding.cpp
  - graph_matching_python_binding_helper.cpp
  - setup.py
- - CMakeLists.txt
  - generate_solver.py
  - horizon_tracking_fwmap.cpp
  - horizon_tracking_MST.cpp
  - horizon_tracking_subgradient.cpp
  - horizon_tracking_uai_input.cpp
- - CMakeLists.txt
  - ldp_batch_process.cxx
  - ldp_cut_factor.cxx
  - ldp_directed_graph.cxx
  - ldp_functions.cxx
  - ldp_instance.cxx
  - ldp_interval_connection.cxx
  - ldp_path_factor.cxx
  - ldp_paths_extractor.cxx
  - ldp_python.cxx
  - ldp_two_layer_graph.cxx
  - lifted_disjoint_paths_input.cpp
  - lifted_disjoint_paths_text_input.cpp
  - solveFromFiles.py
  - solveFromFilesForIntervals.py
  - solveFromVectors.py
  - solveFromVectorsTwoGraphs.py
  - solveInBatches.py
- - CMakeLists.txt
  - convert_dimacs_graph_cut_max_flow_to_max_cut.cpp
  - convert_dimacs_qpbo_max_flow_to_max_cut.cpp
  - generate_solvers.py
  - max_cut_cycle_packing.cpp
  - max_cut_cycle_packing_text_input.cpp
  - max_cut_cycle_qpbo_uai_input.cpp
  - max_cut_cycle_text_input.cpp
  - max_cut_greedy_additive_edge_contraction.cpp
  - max_cut_greedy_additive_edge_contraction_text_input.cpp
  - max_cut_local_search.cpp
  - max_cut_odd_bicycle_wheel_packing.cpp
  - max_cut_odd_bicycle_wheel_packing_text_input.cpp
  - max_cut_odd_bicycle_wheel_qpbo_uai_input.cpp
  - max_cut_odd_bicycle_wheel_text_input.cpp
  - max_cut_sahni_gonzalez.cpp
  - max_cut_sahni_gonzalez_text_input.cpp
  - max_cut_text_input.cpp
- - CMakeLists.txt
  - convert_dimacs_graph_cut_max_flow_to_mrf_uai.cpp
  - convert_dimacs_qpbo_max_flow_to_mrf_uai.cpp
  - convert_opengm_mrf_to_lp.cpp
  - convert_opengm_mrf_to_uai.cpp
  - convert_uai_mrf_to_lp.cpp
  - dimacs_max_flow_input.cpp
  - FWMAP_opengm.cpp
  - FWMAP_uai.cpp
  - generate_solvers.py
  - mplp_opengm.cpp
  - mplp_uai.cpp
  - mrf_opengm_input.cpp
  - mrf_uai_input.cpp
  - pairwise_Potts_factor.cpp
  - pairwise_simplex_factor.cpp
  - qpbo_dimacs.cpp
  - qpbo_uai.cpp
  - srmp_opengm.cpp
  - srmp_opengm_combiLP.cpp
  - srmp_opengm_tightening.cpp
  - srmp_uai.cpp
  - srmp_uai_combiLP.cpp
  - srmp_uai_tightening.cpp
  - ternary_simplex_factor.cpp
- - andres_graph_utility.hxx
  - CMakeLists.txt
  - convert_andres_multicut_grid_graph_to_text.cpp
  - convert_andres_multicut_to_text.cpp
  - convert_multigraph_matching_to_multicut.cpp
  - convert_opengm_multicut_to_text.cpp
  - convert_simple_multicut_hdf5_to_text.cpp
  - correlation_clustering_instance.cpp
  - generate_solvers.py
  - lifted_multicut_h5.cpp
  - lifted_multicut_h5_grid.cpp
  - lifted_multicut_text.cpp
  - multicut_andres_input.cpp
  - multicut_balanced_edge_contraction.cpp
  - multicut_bec_text_input.cpp
  - multicut_cycle_andres_input.cpp
  - multicut_cycle_opengm_input.cpp
  - multicut_cycle_packing.cpp
  - multicut_cycle_packing_parallel.cpp
  - multicut_cycle_packing_text_input.cpp
  - multicut_cycle_packing_text_input_parallel.cpp
  - multicut_cycle_text_input.cpp
  - multicut_factors_messages.cpp
  - multicut_gaec_parallel_text_input.cpp
  - multicut_gaec_text_input.cpp
  - multicut_greedy_additive_edge_contraction.cpp
  - multicut_greedy_additive_edge_contraction_andres_input.cpp
  - multicut_greedy_additive_edge_contraction_parallel.cpp
  - multicut_greedy_edge_fixation.cpp
  - multicut_greedy_edge_fixation_text_input.cpp
  - multicut_higher_order.cpp
  - multicut_higher_order_bicycle_wheel.cpp
  - multicut_higher_order_odd_wheel.cpp
  - multicut_instance.cpp
  - multicut_kernighan_lin.cpp
  - multicut_local_search.cpp
  - multicut_local_search_text_input.cpp
  - multicut_message_passing_parallel.cpp
  - multicut_message_passing_text_input_parallel.cpp
  - multicut_odd_bicycle_wheel_andres_input.cpp
  - multicut_odd_bicycle_wheel_opengm_input.cpp
  - multicut_odd_bicycle_wheel_packing.cpp
  - multicut_odd_bicycle_wheel_text_input.cpp
  - multicut_odd_wheel_andres_input.cpp
  - multicut_odd_wheel_opengm_input.cpp
  - multicut_odd_wheel_packing.cpp
  - multicut_odd_wheel_packing_text_input.cpp
  - multicut_odd_wheel_text_input.cpp
  - multicut_opengm_input.cpp
  - multicut_opengm_srmp_cycle.cpp
  - multicut_opengm_srmp_cycle_odd_wheel.cpp
  - multicut_opengm_srmp_cycle_odd_wheel_odd_bicycle_wheel.cpp
  - multicut_python_binding.cpp
  - multicut_srmp.cpp
  - multicut_text_input.cpp
  - sorted_multicut_sequential_edge_fixation_text.cpp
  - transform_multigraph_matching.cpp
- - CMakeLists.txt
  - evaluate_multigraph_matching.cpp
  - generate_multigraph_matching_solvers.py
  - multigraph_matching_input.cpp
  - multigraph_matching_instance.cpp
  - multigraph_matching_linear.cpp
  - multigraph_matching_mcf.cpp
  - multigraph_matching_mcf_inter_quadratic_messages.cpp
  - multigraph_matching_mp.cpp
  - multigraph_matching_python_binding.cpp
  - multigraph_matching_synchronization.cpp
  - multigraph_matching_tightening_mcf.cpp
  - multigraph_matching_tightening_mcf_inter_quadratic_message.cpp
  - multigraph_matching_tightening_mp.cpp
  - multigraph_matching_triplet_consistency_factor.cpp
  - multigraph_matching_universe_frank_wolfe.cpp
  - multigraph_matching_universe_fw.cpp
  - multigraph_matching_universe_koopman_beckmans.cpp
- - CMakeLists.txt
  - multiway_cut_gaec.cpp
  - multiway_cut_instance.cpp
  - multiway_cut_python_binding.cpp
- CMakeLists.txt
- - CMakeLists.txt
  - test_asymmetric_multiway_cut_gaec.cpp
  - test_asymmetric_multiway_cut_instance.cpp
  - test_asymmetric_multiway_cut_parser.cpp
- - CMakeLists.txt
  - test_bdd_bipartite_matching_problem.cpp
  - test_bdd_chain_graph.cpp
  - test_bdd_grid_graph.cpp
  - test_ILP_input_export.cpp
  - test_ILP_input_reordering.cpp
  - test_ILP_input_to_bdd.cpp
  - test_ILP_parser.cpp
  - test_random_chains_bdd.cpp
  - test_random_inequality_to_bdd.cpp
  - test_single_bdd_inference.cpp
  - test_two_bdd_inference.cpp
- - CMakeLists.txt
  - generate_random_graph_matching_problem.h
  - generate_random_label_set.hxx
  - koopmans_beckmann_test_input.cpp
  - test_graph_matching_input_export.cpp
  - test_graph_matching_instance_python_construction.py
  - test_graph_matching_instance_python_input_evaluation.py
- - CMakeLists.txt
  - data_max_potential_chains_test.hxx
  - data_max_potential_grids_test.hxx
  - horizon_tracking_factor_test.cpp
  - horizon_tracking_primal_propagation_test.cpp
  - horizon_tracking_test_helper.hxx
  - max_potential_on_chain_test.cpp
  - max_potential_uai_chain_test.cpp
  - max_potential_uai_grid_chains_decompose_test.cpp
  - test.h
- - CMakeLists.txt
  - max_cut_cycle_packing_test.cpp
  - max_cut_labeling_test.cpp
  - max_cut_odd_bicycle_wheel_packing_test.cpp
  - max_cut_quintuplet_constructor_test.cpp
  - max_cut_triplet_quintuplet_message_test.cpp
  - transform_binary_Potts_test.cpp
- - binary_pairwise_potential_test.cpp
  - CMakeLists.txt
  - combiLP.cpp
  - cycle_inequalities.cpp
  - dd_ilp_gurobi.cpp
  - dimacs_max_flow_input_test.cpp
  - generate_export_read_binary_MRF_instance_test.cpp
  - mrf_chain_test.cpp
  - mrf_read_uai_file.cpp
  - mrf_sat_rounding.cpp
  - mrf_tightening.cpp
  - mrf_tree.cpp
  - mrf_tree_decomposition.cpp
  - potts_factor.cpp
  - simplex.cpp
  - simplex_marginalization.cpp
  - test_mrf.hxx
  - test_transform_binary_MRF_to_Potts.cpp
  - transform_max_flow_test.cpp
- - CMakeLists.txt
  - test_multicut_cycle_packing.cpp
  - test_multicut_message_passing_parallel.cpp
  - test_multicut_odd_bicycle_wheel_packing.cpp
  - test_multicut_odd_wheel_packing.cpp
  - test_triangulation.cpp
- - CMakeLists.txt
  - minimal_synchronization_example.cpp
  - multigraph_matching_consistency_constraint_test.cpp
  - multigraph_matching_transformation.cpp
  - test_multigraph_matching_instance_python_construction.py
  - test_multigraph_matching_min_marginals_triplet_consistency.cpp
  - test_multigraph_matching_synchronization.cpp
- CMakeLists.txt
- generate_random_graph.hxx
- graph_test.cpp
- serialization.cpp
- test_bfs_ordering.cpp
- test_commutation_matrix.cpp
- test_cuthill_mckee.cpp
- test_FWMAP.cpp
- test_message.hxx
- test_message_passing_schedule.cpp
- test_model.cpp
- test_model.hxx
- test_polynomial_functions.cpp
- test_reparametrization_recognition.cpp
- test_three_dimensional_variable_array.cpp
- test_topological_sort.cpp
- test_two_dimensional_variable_array.cpp
- test_weight_computation.cpp
- vector.cpp
.gitignore
.gitmodules
.travis.yml
CMakeLists.txt
README.md
setup.py

// repository documentation

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LPMP
========

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].

## Solvers
We provide a range of solvers for various discrete optimization problems, including
* **[Discrete graphical models](/include/mrf)**,
* **[Multicut](/include/multicut)**, [3]
* **[Max-cut](/include/max_cut)**, 
* **[Graph matching](include/graph_matching)**, [4]
* **[Multi-graph matching](/include/multigraph_matching)**, [5]
* **[Discrete graphical models with bottleneck terms](/include/horizon_tracking)**, [6]
* **[Lifted disjoint paths](include/lifted_disjoint_paths)**.

Benchmark problems for various solvers above can be found in [datasets](/datasets).

## Optimization techniques
Optimization techniques include
* **Messsage passing [1]**,
* **Subgradient ascent with a proximal bundle method based on the Frank-Wolfe algorithm [2]**, [Vladimir Kolmogorov's](http://http://pub.ist.ac.at/~vnk/) [original implementation](http://pub.ist.ac.at/~vnk/papers/FWMAP.html).
* An interface to **external solvers** is provided by [DD_ILP](https://github.com/pawelswoboda/DD_ILP).

## Differentiable wrappers

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](https://github.com/martius-lab/blackbox-deep-graph-matching)) or the general [repository](https://github.com/martius-lab/blackbox-backprop) 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`

## Installation
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](https://solarianprogrammer.com/2016/10/07/building-gcc-ubuntu-linux/) for installation instructions).
* HDF5 (install with `apt install libhdf5-serial-dev`)
* cmake (install with `apt install cmake`)

## Documentation

A tutorial on writing a new solver from scratch can be found [here](/doc/Getting-Started.md).
The documentation for using all the existing solvers is in the directory [doc](/doc).

## References
* [1]: [`P. Swoboda, J. Kuske and B. Savchynskyy. A Dual Ascent Framework for Lagrangean Decomposition of Combinatorial Problems. In CVPR 2017.`](http://openaccess.thecvf.com/content_cvpr_2017/html/Swoboda_A_Dual_Ascent_CVPR_2017_paper.html)
* [2]: [`P. Swoboda and V. Kolmogorov. MAP inference via Block-Coordinate Frank-Wolfe Algorithm. In CVPR 2019`](http://openaccess.thecvf.com/content_CVPR_2019/html/Swoboda_MAP_Inference_via_Block-Coordinate_Frank-Wolfe_Algorithm_CVPR_2019_paper.html)
* [3]: [`P. Swoboda and B. Andres. A Message Passing Algorithm for the Minimum Cost Multicut Problem. In CVPR 2017.`](http://openaccess.thecvf.com/content_cvpr_2017/html/Swoboda_A_Message_Passing_CVPR_2017_paper.html)
* [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.`](http://openaccess.thecvf.com/content_cvpr_2017/html/Swoboda_A_Study_of_CVPR_2017_paper.html)
* [5]: [`P. Swoboda, D. Kainmueller, A. Mokarian, C. Theobalt and F. Bernard. A convex approach to multi-graph matching. In CVPR 2019.`](http://openaccess.thecvf.com/content_CVPR_2019/html/Swoboda_A_Convex_Relaxation_for_Multi-Graph_Matching_CVPR_2019_paper.html)
* [6]: [`A. Abbas, P. Swoboda. Bottleneck Potentials in Markov Random Fields. In ICCV 2019.`](http://openaccess.thecvf.com/content_ICCV_2019/html/Abbas_Bottleneck_Potentials_in_Markov_Random_Fields_ICCV_2019_paper.html)
* [7]: [`M. Vlastelica, A. Paulus, V. Musil, G. Martius, M. Rolínek. Differentiation of Blackbox Combinatorial Solvers. In ICLR 2020.`](https://openreview.net/forum?id=BkevoJSYPB)
* [8]: [`M. Rolínek, P. Swoboda, D. Zietlow, A. Paulus, V. Musil, G. Martius. Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers.`](https://arxiv.org/abs/2003.11657)
* [9]: [`A. Abbas, P. Swoboda. Combinatorial Optimization for Panoptic Segmentation: An End-to-End Trainable Approach.`](https://arxiv.org/abs/2106.03188)

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