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Recently, sparse training has emerged as a promising paradigm for efficient deep learning on edge devices. The current research mainly devotes efforts to reducing training costs by further increasing model sparsity. However, increasing sparsity is not always ideal since it will inevitably introduce severe accuracy degradation at an extremely high sparsity level. This paper intends to explore other possible directions to effectively and efficiently reduce sparse training costs while preserving accuracy. To this end, we investigate two techniques, namely, layer freezing and data sieving. First, the layer freezing approach has shown its success in dense model training and fine-tuning, yet it has never been adopted in the sparse training domain. Nevertheless, the unique characteristics of sparse training may hinder the incorporation of layer freezing techniques. Therefore, we analyze the feasibility and potentiality of using the layer freezing technique in sparse training and find it has the potential to save considerable training costs. Second, we propose a data sieving method for dataset-efficient training, which further reduces training costs by ensuring only a partial dataset is used throughout the entire training process. We show that both techniques can be well incorporated into the sparse training algorithm to form a generic framework, which we dub SpFDE. Our extensive experiments demonstrate that SpFDE can significantly reduce training costs while preserving accuracy from three dimensions: weight sparsity, layer freezing, and dataset sieving.