  Utilizing long-range dependency, a concept extensively studied in homogeneous
graphs, remains underexplored in heterogeneous graphs, especially on large
ones, posing two significant challenges: Reducing computational costs while
maximizing effective information utilization in the presence of heterogeneity,
and overcoming the over-smoothing issue in graph neural networks. To address
this gap, we investigate the importance of different meta-paths and introduce
an automatic framework for utilizing long-range dependency on heterogeneous
graphs, denoted as Long-range Meta-path Search through Progressive Sampling
(LMSPS). Specifically, we develop a search space with all meta-paths related to
the target node type. By employing a progressive sampling algorithm, LMSPS
dynamically shrinks the search space with hop-independent time complexity.
Through a sampling evaluation strategy, LMSPS conducts a specialized and
effective meta-path selection, leading to retraining with only effective
meta-paths, thus mitigating costs and over-smoothing. Extensive experiments
across diverse heterogeneous datasets validate LMSPS's capability in
discovering effective long-range meta-paths, surpassing state-of-the-art
methods. Our code is available at https://github.com/JHL-HUST/LMSPS.
