# GLAN: A Graph-based Linear Assignment Network

arXiv: https://arxiv.org/abs/2201.02057 · HTML: https://mlsanity.com/paper/2201.02057/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 43 references that are in the map.
- First posted on arXiv 5 Jan 2022.

## Builds on (most cited first, 15 of 15)

- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [MOT16: A Benchmark for Multi-Object Tracking](https://mlsanity.com/paper/1603.00831/) (2016)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Tracking without bells and whistles](https://mlsanity.com/paper/1903.05625/) (2019)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Deep Affinity Network for Multiple Object Tracking](https://mlsanity.com/paper/1810.11780/) (2018)
- [How To Train Your Deep Multi-Object Tracker](https://mlsanity.com/paper/1906.06618/) (2019)
- [Hierarchical Representation Learning in Graph Neural Networks with Node Decimation Pooling](https://mlsanity.com/paper/1910.11436/) (2019)
- [Graph Edge Convolutional Neural Networks for Skeleton Based Action Recognition](https://mlsanity.com/paper/1805.06184/) (2018)
- [DMM-Net: Differentiable Mask-Matching Network for Video Object Segmentation](https://mlsanity.com/paper/1909.12471/) (2019)
- [Action Recognition via Pose-Based Graph Convolutional Networks with Intermediate Dense Supervision](https://mlsanity.com/paper/1911.12509/) (2019)
- [A Concave Optimization Algorithm for Matching Partially Overlapping Point Sets](https://mlsanity.com/paper/1701.00951/) (2017)

## Built on by (most cited first, 6 of 6)

- [Musical Voice Separation as Link Prediction: Modeling a Musical Perception Task as a Multi-Trajectory Tracking Problem](https://mlsanity.com/paper/2304.14848/) (2023)
- [Decentralized Vision-Based Autonomous Aerial Wildlife Monitoring](https://mlsanity.com/paper/2508.15038/) (2025)
- [DecoderTracker: Decoder-Only Method for Multiple-Object Tracking](https://mlsanity.com/paper/2310.17170/) (2023)
- [Optimal and efficient text counterfactuals using Graph Neural Networks](https://mlsanity.com/paper/2408.01969/) (2024)
- [How to Backpropagate through Hungarian in Your DETR?](https://mlsanity.com/paper/2211.14448/) (2022)
- [Learning-Augmented Scalable Linear Assignment Problem Optimization via Neural Dual Warm-Starts](https://mlsanity.com/paper/2605.09382/) (2026)

## Abstract (arXiv)

Differentiable solvers for the linear assignment problem (LAP) have attracted much research attention in recent years, which are usually embedded into learning frameworks as components. However, previous algorithms, with or without learning strategies, usually suffer from the degradation of the optimality with the increment of the problem size. In this paper, we propose a learnable linear assignment solver based on deep graph networks. Specifically, we first transform the cost matrix to a bipartite graph and convert the assignment task to the problem of selecting reliable edges from the constructed graph. Subsequently, a deep graph network is developed to aggregate and update the features of nodes and edges. Finally, the network predicts a label for each edge that indicates the assignment relationship. The experimental results on a synthetic dataset reveal that our method outperforms state-of-the-art baselines and achieves consistently high accuracy with the increment of the problem size. Furthermore, we also embed the proposed solver, in comparison with state-of-the-art baseline solvers, into a popular multi-object tracking (MOT) framework to train the tracker in an end-to-end manner. The experimental results on MOT benchmarks illustrate that the proposed LAP solver improves the tracker by the largest margin.