The emergence of edge computing and IoT has allowed computational resources closer to the end users, hence improving applications that are latency-sensitive and demand significant resources. Distributed computing is a viable method for advancing computations through parallel tasking across multiple computation nodes. Research has been predominantly focused on the masters and worker paradigm, wherein resource sharing is confined to one-hop neighborhoods. This limitation can disrupt the efficiency of distributed computing, particularly when local resources are scarce or the connectivity is inconsistent. This study offers a unique distributed computing paradigm that expands resource-sharing capabilities beyond local one-hop neighbors by leveraging layered network topologies. We propose a hybrid centralized mixed-integer linear programming optimization method that incorporates a chameleon swarm optimization approach to derive the optimal solutions. The efficacy of the proposed scheme was assessed through theoretical analyses and extensive simulation experiments, which demonstrated its advantages over traditional distributed computing and computation offloading schemes.