# Computing a many-to-many matching with demands and capacities between two sets using the Hungarian algorithm

arXiv: https://arxiv.org/abs/2211.01612 · HTML: https://mlsanity.com/paper/2211.01612/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2022.

## Built on by (most cited first, 1 of 1)

- [STAG-VIO: Stabilized Prompt-to-Geometry Interface for Robust Dynamic Visual--Inertial Odometry](https://mlsanity.com/paper/2411.19289/) (2024)

## Abstract (arXiv)

Given two sets A=a1,a2,...,as and b1,b2,...,bt, a many-to-many matching with demands and capacities (MMDC) between A and B matches each element ai in A to at least αi and at most α'i elements in B, and each element bj in B to at least βj and at most β'j elements in A for all 1=<i<=s and 1=<j<=t. In this paper, we present an algorithm for finding a minimum-cost MMDC between A and B using the well-known Hungarian algorithm.