The rise of the Internet of Things and edge computing has shifted computing resources closer to end-users, benefiting numerous delay-sensitive, computation-intensive applications. To speed up computation, distributed computing is a promising technique that allows parallel execution of tasks across multiple compute nodes. However, current research predominantly revolves around the master-worker paradigm, limiting resource sharing within one-hop neighborhoods. This limitation can render distributed computing ineffective in scenarios with limited nearby resources or constrained/dynamic connectivity. In this paper, we address this limitation by introducing a new distributed computing framework that extends resource sharing beyond one-hop neighborhoods through exploring layered network structures and multi-hop routing. Our framework involves transforming the network graph into a sink tree and formulating a joint optimization problem based on the layered tree structure for task allocation and scheduling. To solve this problem, we propose two exact methods that find optimal solutions and three heuristic strategies to improve efficiency and scalability. The performances of these methods are analyzed and evaluated through theoretical analyses and comprehensive simulation studies. The results demonstrate their promising performances over the traditional distributed computing and computation offloading strategies.

翻译：物联网与边缘计算的兴起将计算资源推向终端用户侧，为众多时延敏感、计算密集的应用带来便利。为加速计算过程，分布式计算作为一种关键技术，允许多个计算节点并行执行任务。然而，现有研究主要围绕主-从范式展开，将资源共享局限在单跳邻域内。这一限制在邻近资源有限或网络连通性受限/动态变化的场景下，可能导致分布式计算效能低下。本文通过提出一种新的分布式计算框架来解决此问题，该框架通过探索分层网络结构与多跳路由，将资源共享扩展至单跳邻域之外。我们的框架将网络图转换为汇点树，并基于分层树结构构建了任务分配与调度的联合优化问题。为解决该问题，我们提出了两种获取最优解的精确方法以及三种提升效率与可扩展性的启发式策略。通过理论分析与全面的仿真研究，对这些方法的性能进行了分析与评估。结果表明，相较于传统分布式计算与计算卸载策略，所提方法展现出更优越的性能。