Existing heterogeneous graph neural networks (HGNNs) have achieved great success in utilizing the rich semantic information in heterogeneous information networks (HINs). However, few works have delved into the utilization of long-range dependencies in HINs, which is extremely valuable as many real-world HINs are sparse, and each node has only a few directly connected neighbors. Although some HGNNs can utilize distant neighbors by stacking multiple layers or leveraging long meta-paths, the exponentially increased number of nodes in the receptive field or the number of meta-paths incurs high computation and memory costs. To address these issues, we investigate the importance of different meta-paths and propose Long-range Dependency based Multi-Layer Perceptron (LDMLP). Specifically, to solve the high-cost problem of leveraging long-range dependencies, LDMLP adopts a search stage to discover effective meta-paths automatically, reducing the exponentially increased number of meta-paths to a constant. To avoid the influence of specific modules on search results, LDMLP utilizes a simple architecture with only multi-layer perceptions in the search stage, improving the generalization of searched meta-paths. As a result, the searched meta-paths not only perform well in LDMLP but also enable other HGNNs like HAN and SeHGNN to perform better. Extensive experiments on eight heterogeneous datasets demonstrate that LDMLP achieves state-of-the-art performance while enjoying high efficiency and generalization, especially on sparse HINs.