2026 Volume 34 Pages 830-842
Graphs play a crucial role in various research fields, including network science, machine learning, and data analysis. Algorithms based on random walks have become popular for information diffusion, target node search, and exploration on graphs. Random walk algorithms can be classified into local and non-local random walks. Local random walks enable transition between adjacent nodes based on predefined probabilities, while non-local random walks enable transitions that extend beyond immediate neighbors. While non-local random walks enable faster graph exploration by reaching beyond immediate neighbors, these methods typically require the agent to have full knowledge of the entire graph and the ability to freely move to any non-adjacent node, which makes them difficult to implement in large-scale networks. The aim of this study is to develop a local random walk that improves graph exploration efficiency by leveraging partial non-local information stored at nodes, without requiring the agent to have global knowledge of the graph structure. Specifically, we propose a random walk called Sprint Walk, in which designated nodes record shortest paths to a small number of non-adjacent nodes (anchor nodes), thereby enabling non-local-like transition behavior through a series of local transitions by the agent. Through simulation experiments, we demonstrate that Sprint Walk significantly reduces search and exploration time compared to classical local random walk algorithms, including the Simple Random Walk (SRW), Biased Random Walk (BiasedRW), Non-Backtracking Random Walk (NBRW), and Self-Avoiding Random Walk (SARW) across nine graph types. Finally, we present an analytical model for Sprint Walk and derive its mean first-passage time and validate it through a numerical example.
