In the context of mobile edge computing, efficiently deploying microservices to reduce finish time and enhance user service quality is a challenging task. However, existing research still has certain deficiencies in considering microservice deployment within edge server clusters and communication link constraints. To address this issue, we propose three microservice deployment strategies by offering flexibility and adaptability for various application scenarios. We initially consider two straightforward scenarios: one with unlimited storage resources under the bandwidth constraint, and the other with unlimited bandwidth resources under the storage constraint. For each of these two scenarios, we introduce a novel enhanced graph construction method and design two optimal solutions. For Scenario 3, which involves complex constraints on server capacity, computational capability, and communication resources, we present an optimization method based on main path partitioning and the simulated annealing algorithm. We effectively tackle challenges arising from server capacity, computational capability, and communication resource limitations. Across multiple experimental setups, our approach significantly improves microservice deployment efficiency and overall performance compared to traditional strategies.