In this paper, we investigate the problem of maximizing the lifetime of robot swarms in wireless networks utilizing a multi-user edge computing system. Robots offload their computational tasks to an edge server, and our objective is to efficiently exploit the correlation between distributed data sources to extend the operational lifetime of the swarm. The optimization problem is approached by selecting appropriate subsets of robots to transmit their sensed data to the edge server. Information theory principles are used to justify the grouping of robots in the swarm network, with data correlation among distributed robot subsets modeled as an undirected graph. We introduce a periodic subset selection problem, along with related and more relaxed formulations such as a graph partitioning problem and a subgraph-level vertex selection problem, to address the swarm lifetime maximization challenge. For additive white Gaussian noise channels, we analyze the theoretical upper bound of the swarm lifetime and propose several algorithms—including the least-degree iterative partitioning algorithm and final vertex search algorithm—to approach this bound. Additionally, we consider the impact of channel diversity on subset selection in flat-fading channels and adapt the algorithm to account for variations in the base station’s channel estimation capabilities. Comprehensive simulation experiments are conducted to evaluate the effectiveness of the proposed methods. Results show that the algorithms achieve a swarm lifetime up to 650% longer than that of benchmark approaches.