No-collision Transportation Maps

This is the repository for the paper "No-collision Transportation Maps", by L. Nurbekyan, A. Iannantuono and A. M. Oberman.

Approximating optimal transportation maps using k-d trees.

Code to reproduce the methods of the aforementioned paper. Included are:

• Example script for typical usage
• Algorithm used build k-d tree used to construct the map
• Testing scripts to generate results and perform a comparison

Experiments

Building k-d trees for constructing no-collision transportation maps were compared to methods implemented in the Python Optimal Transport (POT) library available here.

Prerequisites

The code was developed and tested in Python 3.7.1, NumPy 1.16.3 and SciPy 1.3.0, although it should work with earlier versions. Comparisons were done using POT 0.5.1.

Installing

Download the files or fork the repository, and then run example.py.

Code Author

• Alexander Iannantuono - Development and experimental testing

Bugs

If a bug is found, feel free to contact me or create an issue.

Acknowledgements

I would like to thank:

• NSERC and FRQNT for financial support
• The POT team for their library

Citation

If you use these methods in your scientific work, please cite as

@misc{nurbekyan2019nocollision,
    title={No-collision Transportation Maps},
    author={Levon Nurbekyan and Alexander Iannantuono and Adam M. Oberman},
    year={2019},
    eprint={1912.02317},
    archivePrefix={arXiv},
    primaryClass={math.OC}
}