OptimalBranching.jl is a collection of tools for solving combinatorial optimization problems with branch-and-reduce method. It is written in Julia and features automatically generated branching rules with provable optimality (arXiv: 2412.07685). The rule generation is problem agnostic, and it can be easily extended to other problems. It contains two submodules:

• OptimalBranchingCore.jl: the core algorithms, which convert the problem of searching the optimal branching rule into the problem of searching the optimal set cover.
• OptimalBranchingMIS.jl: the maximum independent set (MIS) problem solver based on the optimal branching algorithms.

Installation

OptimalBranching is a   Julia Language   package. To install OptimalBranching, please open Julia's interactive session (known as REPL) and press ] key in the REPL to use the package mode, then type the following command

pkg> add OptimalBranchingCore  # for the core algorithms

pkg> add OptimalBranching      # for utilities based on the core algorithms

If you have problem to install the package, please file us an issue.

Get started

julia> using OptimalBranching, OptimalBranching.OptimalBranchingMIS.Graphs

julia> graph = smallgraph(:tutte)
{46, 69} undirected simple Int64 graph

julia> mis_branch_count(graph)
(19, 2)

In this example, the maximum independent set size of the Tutte graph is 19, and the optimal branching strategy only generates 2 branches in the branching tree.

For advanced usage, please refer to the documentation.

How to Contribute

If you find any bug or have any suggestion, please open an issue.

Citation

If you find this package useful in your research, please cite the relevant paper in the CITATION.bib file.