Multi-access edge computing (MEC) is emerging to improve the quality of experience of mobile devices including internet of things (IoT) sensors by offloading computing intensive tasks to MEC servers. Existing MEC-enabled cooperative computation offloading works focus on the optimization of total energy consumption, while fail to exploit multi-relay diversity and min-max fairness of energy consumption on participated sensors. We explore a typical wireless sensor network with multi-source, multi-relay and one edge server, where relay nodes can provide both cooperative communication and computation services. We divide the energy efficiency optimization problem into two sub-problems: one is to minimize the weighted average total energy consumption per time slot, and the other is to minimize the maximum weighted energy consumption. For the first sub-problem, we propose an optimal algorithm named as OTCA based on bipartite matching. For the second sub-problem, a greedy algorithm named as GAF is proposed with an approximation ratio of (1 + ϵ), where ϵ is a small positive constant. Extensive numerical results show that, OTCA outperforms the baseline algorithms by
\(26.7\%\sim 77.4\% \)
on the average total weighted energy consumption while GAF outperforms benchmark algorithms by
\(30.7\%\sim 84.4\% \)
. NS-3 simulation experiments comply with numerical results.