Joint Scheduling and Multiflow Maximization in Wireless Networks

2025-09-17

AI Summary

This work addresses the NP-hard joint scheduling and max-min fair (MMF) multi-flow transmission problem in 6G large-scale multi-hop wireless networks supporting network coding, under multi-source multi-sink scenarios. Method: We propose an iterative joint optimization framework that avoids precomputing the complete rate region, integrating network coding, graph-theoretic modeling, and joint optimization theory to co-optimize scheduling policies and multi-flow allocation. Contribution/Results: We theoretically prove finite-step convergence to the global optimum. Simulations demonstrate significantly improved computational efficiency and scalability over conventional approaches, with robust performance under high propagation delay (e.g., underwater networks) and general multicast topologies. To the best of our knowledge, this is the first method enabling efficient, scalable, and exact computation of the optimal MMF solution for such networks.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Towards the development of 6G mobile networks, it is promising to integrate a large number of devices from multi-dimensional platforms, and it is crucial to have a solid understanding of the theoretical limits of large-scale networks. We revisit a fundamental problem at the heart of network communication theory: the maximum multiflow (MMF) problem in multi-hop networks, with network coding performed at intermediate nodes. To derive the exact-optimal solution to the MMF problem (as opposed to approximations), conventional methods usually involve two steps: first calculate the scheduling rate region, and then find the maximum multiflow that can be supported by the achievable link rates. However, the NP-hardness of the scheduling part makes solving the MMF problem in large networks computationally prohibitive. In this paper, while still focusing on the exact-optimal solution, we provide efficient algorithms that can jointly calculate the scheduling rate region and solve the MMF problem, thereby outputting optimal values without requiring the entire scheduling rate region. We theoretically prove that our algorithms always output optimal solutions in a finite number of iterations, and we use various simulation results to demonstrate our advantages over conventional approaches. Our framework is applicable to the most general scenario in multi-source multi-sink networks: the multiple multicast problem with network coding. Moreover, by employing a graphical framework, we show that our algorithm can be extended to scenarios where propagation delays are large (e.g., underwater networks), in which recent studies have shown that the scheduling rate region can be significantly improved by utilizing such delays.

Problem

• Exact-optimal maximum multiflow problem in multi-hop networks
• Jointly calculating scheduling rate region and multiflow efficiently
• Overcoming NP-hard scheduling complexity for large-scale networks

Innovation

• Joint scheduling and multiflow optimization algorithm
• Graphical framework for large propagation delays
• Efficient exact-optimal solution without full scheduling