Local matching indicators for transport problems with concave costs

TL;DR

This paper introduces a new class of local indicators that efficiently compute optimal transport plans for distributions with concave costs, significantly reducing computational complexity regardless of demand and supply sizes.

Contribution

The paper presents a novel class of local matching indicators that enable efficient computation of optimal transport plans with concave costs, independent of the number of demands and supplies.

Findings

Indicators have low, demand-independent computational cost.

Hierarchical use of indicators leads to an efficient algorithm.

Method effectively handles arbitrary distributions with concave costs.

Abstract

In this paper, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of N demands and M supplies in 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.