## 4 Methodology
### Domain Clustering Based on Multi-Path Transmission
#### 4.2.6 Problem Modeling and Optimization Algorithm Design
Next, it adjusts the resource utility through Nash bargaining optimization using the computed fairness factor \(\phi\) and domain information \(D\), to ensure fair and efficient resource allocation (Line 9). After that, the algorithm solves the dual optimization problem to obtain the final optimal power allocation \(P^{*}\) and bandwidth allocation \(B^{*}\) under system constraints (Line 11). Finally, it returns the optimized task allocation \(A\), power allocation \(P^{*}\), and bandwidth allocation \(B^{*}\) as the output (Line 12). ```
1:Setellite node set \(N\), task set \(T\), network topology \(G(V,E)\), resource capacity \(R\)
2:Task allocation \(A\), power allocation \(P\), bandwidth allocation \(B\)
3:Step 1: Preprocessing (Apply NBGRA Algorithm 1)
4:\([U,\mu^{E},R^{h},Y]\leftarrow\mathrm{Preprocess}(N,T,G,R)\)
5:Step 2: Domain Clustering and Local Shapley Approximation (Apply IRA-LM Algorithm 2)
6:\(D\leftarrow\mathrm{ClusterDomains}(N,G,\mathrm{criteria})\)
7:for all domain \(D_{k}\in D\)do
8:\(\phi_{i}=\mathrm{ApproximateShapley}(D_{k})\)
9:endfor
10:Step 3: Nash Bargaining Resource Adjustment (Apply PF-RARO Algorithm 3)
11:\(U_{opt}\leftarrow\mathrm{NashBargaining}(U,\phi,D)\)
12:Step 4: Final Resource Optimization (Apply CRA Algorithm 4)
13:\([P^{*},B^{*}]\leftarrow\mathrm{DualOptimization}(U_{opt},R)\)
14:return\(A,P^{*},B^{*}\)
```

**Algorithm 5** CMPT: Fairness-Aware Resource Allocation with Local Shapley Approximation

## 5 Experimental Results

This study used the Common Satellite Tool Kit (CSTK) as the simulation environment to accurately model a dynamic satellite network scenario. To address the challenges of resource allocation and task scheduling under fluctuating network topologies and varying traffic demands, we developed specialized modules within the simulation system, including satellite orbit simulation, communication link management, and task scheduling mechanisms. Leveraging these modules, we constructed a series of comprehensive experiments that evaluated the performance of the proposed Coding Multi-Path Theory (CMPT) method against established comparative algorithms across different satellite configurations and task loads. The experimental setup encompassed diverse datasets, multiple satellite scales, and a range of task priorities, to thoroughly assess CMPT's effectiveness and scalability in real-world dynamic network conditions. The basic simulation interface of CSTK is shown in Figure 3. The system integrates orbit dynamics modeling, link-state awareness, and task coordination scheduling. As illustrated, the platform features a central Earth model (blue sphere) surrounded by dynamically rendered satellite constellation trajectories (yellow/green orbital lines). The left panel provides real-time updates on satellite node states (e.g., ID, longitude, latitude, and attitude angles), while the bottom timeline synchronizes the simulation progress with real-world timestamps. Leveraging three-dimensional visualization and parameter-coupling mechanisms, the platform enables interpretable representation of dynamic network topologies (orbital period variations), quantitative monitoring of multi-path resource states (bandwidth/latency parameters embedded in satellite attribute panels), and spatiotemporal consistency verification of task scheduling processes (scenario-simulated time alignment). ### Dataset Details and Scenario Description

The dataset used in this study encompassed various parameters required for satellite network resource allocation and scheduling, specifically including each satellite node's resource vector \(\mathbf{R}_{i}=(C_{i},B_{i},Q_{i})\), corresponding to computational capacity \(C_{i}\), bandwidth \(B_{i}\) and storage capacity \(Q_{i}\). Here, \(C_{i}\) represents the computational capacity of satellite node \(i\) and is a non-negative real number; \(B_{i}\) denotes the bandwidth, also a non-negative real number; and \(Q_{i}\) indicates the storage capacity, similarly a non-negative real number.