Local matching indicators for transport with concave costs

TL;DR

This paper introduces a new class of local matching indicators that efficiently compute optimal transport plans with concave costs for arbitrary demand and supply distributions on the real line, with computational costs independent of the number of points.

Contribution

The paper presents a novel class of indicators that enable efficient computation of optimal transport plans with concave costs, independent of the problem size.

Findings

Indicators have low computational cost and are independent of N.

Hierarchical use of indicators leads to an efficient algorithm.

Applicable to arbitrary distributions of demands and supplies.

Abstract

In this note, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of $N$ demands and $N$ supplies in $\mathbf{R}$ in the case where the cost function is concave. The computational cost of these indicators is small and independent of $N$. A hierarchical use of them enables to obtain an efficient algorithm.