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Fueled by advances in distributed deep learning (DDL), recent years have witnessed a rapidly growing demand for resource-intensive distributed/parallel computing to process DDL computing jobs. To resolve network communication bottleneck and load balancing issues in distributed computing, the so-called ``ring-all-reduce'' decentralized architecture has been increasingly adopted to remove the need for dedicated parameter servers. To date, however, there remains a lack of theoretical understanding on how to design resource optimization algorithms for efficiently scheduling ring-all-reduce DDL jobs in computing clusters. This motivates us to fill this gap by proposing a series of new resource scheduling designs for ring-all-reduce DDL jobs. Our contributions in this paper are three-fold: i) We propose a new resource scheduling analytical model for ring-all-reduce deep learning, which covers a wide range of objectives in DDL performance optimization (e.g., excessive training avoidance, energy efficiency, fairness); ii) Based on the proposed performance analytical model, we develop an efficient resource scheduling algorithm called GADGET (greedy ring-all-reduce distributed graph embedding technique), which enjoys a provable strong performance guarantee; iii) We conduct extensive trace-driven experiments to demonstrate the effectiveness of the GADGET approach and its superiority over the state of the art.