# Control Laguerre Tessellation: Semi-discrete Optimal Transport Over Control Systems

arXiv: https://arxiv.org/abs/2607.09139 · HTML: https://mlsanity.com/paper/2607.09139/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 10 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [Convergence of a Newton algorithm for semi-discrete optimal transport](https://mlsanity.com/paper/1603.05579/) (2016)
- [A Generative Model for Texture Synthesis based on Optimal Transport between Feature Distributions](https://mlsanity.com/paper/2007.03408/) (2020)
- [Prediction and Optimal Feedback Steering of Probability Density Functions for Safe Automated Driving](https://mlsanity.com/paper/2009.09055/) (2020)
- [Optimal transport: discretization and algorithms](https://mlsanity.com/paper/2003.00855/) (2020)
- [Optimal Transport-based Coverage Control for Swarm Robot Systems: Generalization of the Voronoi Tessellation-based Method](https://mlsanity.com/paper/2011.08337/) (2020)
- [The boundary method for semi-discrete optimal transport partitions and Wasserstein distance computation](https://mlsanity.com/paper/1702.03517/) (2017)
- [Lagrangian discretization of variational mean field games](https://mlsanity.com/paper/2010.11519/) (2020)
- [A Controlled Mean Field Model for Chiplet Population Dynamics](https://mlsanity.com/paper/2303.10564/) (2023)
- [2D Density Control of Micro-Particles using Kernel Density Estimation](https://mlsanity.com/paper/2209.03550/) (2022)
- [Solving Semi-Discrete Optimal Transport Problems: star shapedeness and Newton's method](https://mlsanity.com/paper/2310.07489/) (2023)

## Abstract (arXiv)

We study the optimal transport of optimally controlled agents from a compactly supported absolutely continuous source to a discrete target measure. The ground cost for the transport is induced by the optimal cost of the agents' motion. When this ground cost satisfies the twist condition, the optimal transport map is given almost everywhere in terms of a Laguerre tessellation of the state space. We refer to this control-theoretic generalization of Laguerre tessellation as Control Laguerre Tessellation (CLT), and illustrate it for two ground costs induced by linear controlled agents with minimum energy and minimum time objectives.