This project is the rewrite of pyLAPJV which supports Python 3 and updates the core code. The performance is twice as high as the original thanks to the optimization of the augmenting row reduction phase using Intel AVX2 intrinsics. It is a native Python 3 module and does not work with Python 2.x, stick to pyLAPJV otherwise.
Linear assignment problem is the bijection between two sets with equal cardinality which optimizes the sum of the individual mapping costs taken from the fixed cost matrix. It naturally arises e.g. when we want to fit t-SNE results into a rectangular regular grid. See this awesome notebook for the details about why LAP matters: CloudToGrid.
Jonker-Volgenant algorithm is described in the paper:
R. Jonker and A. Volgenant, "A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems," Computing, vol. 38, pp. 325-340, 1987.
This paper is not publicly available though a brief description exists on sciencedirect.com. JV is faster in than the Hungarian algorithm in practice, though the complexity is the same - O(n3).
The C++ source of the algorithm comes from http://www.magiclogic.com/assignment.html It has been reworked and partially optimized with OpenMP 4.0 SIMD.
pip3 install lapjv
Tested on Linux and Windows. macOS is not supported, please do not report macOS build errors in the issues. Feel free to PR macOS support, but I warn that it will be a rough ride.
Refer to test.py for the complete code.
from lapjv import lapjv
row_ind, col_ind, _ = lapjv(cost_matrix)
The assignment matrix by row is row_ind: the value at n-th place is the assigned column index to the n-th row.
col_ind is the reverse of row_ind: mapping from columns to row indexes.
Note: a bijection is only possible for sets with equal cardinality. If you need to map A vectors to B vectors, derive the square symmetric (A+B) x (A+B) matrix: take the first A rows and columns from A and the remaining [A..A+B] rows and columns from B. Set the A->A and B->B costs to some maximum distance value, big enough so that you don't see assignment errors.
This error appears if your CPU does not support the AVX2 instruction set. We do not ship builds for different CPUs so you need to build the package yourself:
pip3 install git+https://github.com/src-d/lapjv
NAN-s in the cost matrix lead to completely undefined result. It is the caller's responsibility to check them.
MIT Licensed,see LICENSE
FAQs
Linear sum assignment problem solver using Jonker-Volgenant algorithm.
We found that lapjv demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 1 open source maintainer collaborating on the project.
Did you know?
Socket for GitHub automatically highlights issues in each pull request and monitors the health of all your open source dependencies. Discover the contents of your packages and block harmful activity before you install or update your dependencies.
Security News
Research
The Socket Research Team breaks down a malicious wrapper package that uses obfuscation to harvest credentials and exfiltrate sensitive data.
Research
Security News
Attackers used a malicious npm package typosquatting a popular ESLint plugin to steal sensitive data, execute commands, and exploit developer systems.
Security News
The Ultralytics' PyPI Package was compromised four times in one weekend through GitHub Actions cache poisoning and failure to rotate previously compromised API tokens.