The field of graph theory is shifting towards incorporating temporal information, which is crucial in real-world applications such as transportation networks and data analysis. Researchers are developing efficient algorithms for computing paths in temporal graphs, including beer paths that capture the option of visiting points of interest prior to reaching the final destination. Additionally, there is a growing interest in generating temporal simple path graphs, which are subgraphs consisting of all temporal simple paths from a source vertex to a target vertex within a given time interval. Furthermore, constructing sparse navigable graphs is becoming increasingly important for graph-based nearest neighbor search methods. Notable papers in this area include:

• A study on beer paths in temporal graphs, which proposes efficient algorithms for computing earliest-arrival, latest-departure, fastest, and shortest temporal beer paths.
• A paper on efficient temporal simple path graph generation, which proposes a method named Verification in Upper-bound Graph to accelerate the processing of temporal simple paths.
• A work on efficiently constructing sparse navigable graphs, which presents an algorithm with provable guarantees for search graph construction, achieving a significant improvement over the naive greedy algorithm.