Training a deep neural network (DNN) requires substantial computational and memory requirements. It is common to use multiple devices to train a DNN to reduce the overall training time. There are several choices to parallelize each layer in a DNN. Exhaustively searching this list to find an optimal parallelization strategy is prohibitively time consuming and impractical. The standard practice is to use data parallelism because of its simplicity. However, data parallelism is often sub-optimal, and suffers from poor performance and high memory requirement. Expert-designed strategies have been proposed on a case-by-case basis using domain specific knowledge. These expert-designed strategies do not generalize well to DNNs other than the ones for which they were designed, and are not always necessarily the best choice. In this paper, we propose an approach to automatically find efficient parallelization strategies for DNNs from their computation graphs. We present an efficient algorithm to compute these strategies within a reasonable time in practice. We evaluate the effectiveness of our approach on various DNNs. We also compare the performance of the strategies identified by our approach against data parallelism, expert-designed strategies, and the state-of-the-art approaches. Our results show that the strategies found using our approach outperform the baseline data parallelism strategy in all the cases. In addition, our strategies achieve better performance than the expert-designed strategies and the state-of-the-art approaches.