Document Open Access Logo

Approximating Optimal Transport With Linear Programs

Author Kent Quanrud

PDF
Thumbnail PDF

File

OASIcs.SOSA.2019.6.pdf
  • Filesize: 437 kB
  • 9 pages

Document Identifiers

Author Details

Kent Quanrud

Cite AsGet BibTex

Kent Quanrud. Approximating Optimal Transport With Linear Programs. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 6:1-6:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/OASIcs.SOSA.2019.6

Abstract

In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation algorithms for optimal transport.
Keywords
  • optimal transport
  • fast approximations
  • linear programming

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Zeyuan Allen Zhu and Lorenzo Orecchia. Nearly-Linear Time Positive LP Solver with Faster Convergence Rate. In Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC 2015, Portland, OR, USA, June 14-17, 2015, pages 229-236, 2015. Google Scholar
  2. Jason Altschuler, Jonathan Weed, and Philippe Rigollet. Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration. In Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, 4-9 December 2017, Long Beach, CA, USA, pages 1961-1971, 2017. Google Scholar
  3. Jose Blanchet, Arun Jambulapati, Carson Kent, and Aaron Sidford. Towards Optimal Running Times for Optimal Transport. CoRR, abs/1810.07717, 2018. URL: http://arxiv.org/abs/1810.07717.
  4. Deeparnab Chakrabarty and Sanjeev Khanna. Better and Simpler Error Analysis of the Sinkhorn-Knopp Algorithm for Matrix Scaling. In 1st Symposium on Simplicity in Algorithms, SOSA 2018, January 7-10, 2018, New Orleans, LA, USA, pages 4:1-4:11, 2018. Google Scholar
  5. Chandra Chekuri and Kent Quanrud. Near-Linear Time Approximation Schemes for some Implicit Fractional Packing Problems. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 801-820, 2017. Google Scholar
  6. Chandra Chekuri and Kent Quanrud. Randomized MWU for Positive LPs. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, LA, USA, January 7-10, 2018, pages 358-377, 2018. Google Scholar
  7. Michael B. Cohen, Aleksander Madry, Dimitris Tsipras, and Adrian Vladu. Matrix Scaling and Balancing via Box Constrained Newton’s Method and Interior Point Methods. In 58th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2017, Berkeley, CA, USA, October 15-17, 2017, pages 902-913, 2017. Google Scholar
  8. Marco Cuturi. Sinkhorn distances: Lightspeed computation of optimal transport. In Advances in Neural Information Processing Systems 26: 27th Annual Conference on Neural Information Processing Systems 2013. Proceedings of a meeting held December 5-8, 2013, Lake Tahoe, Nevada, United States., pages 2292-2300, 2013. Google Scholar
  9. Pavel Dvurechensky, Alexander Gasnikov, and Alexey Kroshnin. Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn’s Algorithm. In Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholmsmässan, Stockholm, Sweden, July 10-15, 2018, pages 1366-1375, 2018. Google Scholar
  10. Christos Koufogiannakis and Neal E. Young. A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear Programs. Algorithmica, 70(4):648-674, 2014. Preliminary version in FOCS 2007. Google Scholar
  11. Yin Tat Lee and Aaron Sidford. Path Finding Methods for Linear Programming: Solving Linear Programs in Õ(√rank) Iterations and Faster Algorithms for Maximum Flow. In 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, Philadelphia, PA, USA, October 18-21, 2014, pages 424-433, 2014. Google Scholar
  12. Michael W. Mahoney, Satish Rao, Di Wang, and Peng Zhang. Approximating the Solution to Mixed Packing and Covering LPs in Parallel Õ(ε^-3) time. In 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, July 11-15, 2016, Rome, Italy, pages 52:1-52:14, 2016. Google Scholar
  13. Jonah Sherman. Generalized Preconditioning and Undirected Minimum-Cost Flow. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 772-780, 2017. Google Scholar
  14. Richard Sinkhorn and Paul Knopp. Concerning nonnegative matrices and doubly stochastic matrices. Pacific Journal of Mathematics, 21(2):343-348, 1967. Google Scholar
  15. Cédric Villani. Topics in Optimal Transportation, volume 58 of Graduate Studies in Mathematics. American Mathematical Society, 2003. Google Scholar
  16. Cédric Villani. Optimal transport: old and new, volume 338 of Grundlehren der mathematischen Wissenschaften. Springer, Berlin, Heidelberg, 2009. Google Scholar
  17. Neal E. Young. Nearly Linear-Time Approximation Schemes for Mixed Packing/Covering and Facility-Location Linear Programs. CoRR, abs/1407.3015, 2014. URL: http://arxiv.org/abs/1407.3015.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact