# Twin Sorting Dynamic Programming Assisted User Association and Wireless Bandwidth Allocation for Hierarchical Federated Learning

arXiv: https://arxiv.org/abs/2408.09076 · HTML: https://mlsanity.com/paper/2408.09076/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 17 Aug 2024.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Federated Learning in Mobile Edge Networks: A Comprehensive Survey](https://mlsanity.com/paper/1909.11875/) (2019)
- [Client-Edge-Cloud Hierarchical Federated Learning](https://mlsanity.com/paper/1905.06641/) (2019)
- [Hierarchical Federated Learning Across Heterogeneous Cellular Networks](https://mlsanity.com/paper/1909.02362/) (2019)
- [Federated Learning over Wireless Networks: Convergence Analysis and Resource Allocation](https://mlsanity.com/paper/1910.13067/) (2019)
- [Convergence Time Optimization for Federated Learning over Wireless Networks](https://mlsanity.com/paper/2001.07845/) (2020)
- [HFEL: Joint Edge Association and Resource Allocation for Cost-Efficient Hierarchical Federated Edge Learning](https://mlsanity.com/paper/2002.11343/) (2020)
- [Hierarchical Federated Learning with Quantization: Convergence Analysis and System Design](https://mlsanity.com/paper/2103.14272/) (2021)
- [Multi-Stage Hybrid Federated Learning over Large-Scale D2D-Enabled Fog Networks](https://mlsanity.com/paper/2007.09511/) (2020)
- [Mobility-Aware Cluster Federated Learning in Hierarchical Wireless Networks](https://mlsanity.com/paper/2108.09103/) (2021)
- [HiFlash: Communication-Efficient Hierarchical Federated Learning with Adaptive Staleness Control and Heterogeneity-aware Client-Edge Association](https://mlsanity.com/paper/2301.06447/) (2023)
- [Multi-Edge Server-Assisted Dynamic Federated Learning with an Optimized Floating Aggregation Point](https://mlsanity.com/paper/2203.13950/) (2022)
- [Energy-Aware Edge Association for Cluster-based Personalized Federated Learning](https://mlsanity.com/paper/2202.02727/) (2022)
- [Time Minimization in Hierarchical Federated Learning](https://mlsanity.com/paper/2210.04689/) (2022)
- [Online User-AP Association with Predictive Scheduling in Wireless Caching Networks](https://mlsanity.com/paper/2008.00161/) (2020)
- [Optimizing User Association and Spectrum Allocation in HetNets: A Utility Perspective](https://mlsanity.com/paper/1412.5731/) (2014)
- [Privacy-Preserving Joint Edge Association and Power Optimization for the Internet of Vehicles via Federated Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2301.11014/) (2023)

## Abstract (arXiv)

In this paper, we study user association and wireless bandwidth allocation for a hierarchical federated learning system that consists of mobile users, edge servers, and a cloud server. To minimize the length of a global round in hierarchical federated learning with equal bandwidth allocation, we formulate a combinatorial optimization problem. We design the twin sorting dynamic programming (TSDP) algorithm that obtains a globally optimal solution in polynomial time when there are two edge servers. In addition, we put forward the TSDP-assisted algorithm for user association when there are three or more edge servers. Furthermore, given a user association matrix, we formulate and solve a convex optimization problem for optimal wireless bandwidth allocation. Simulation results show that the proposed approach outperforms a number of alternative schemes.