This tool shows the core ideas of the Duan-Mao algorithm on a procedurally generated map. Instead of a slow, exhaustive search, it first partitions the graph, selects random pivots, and runs a fast, parallel expansion to quickly explore the space. Finally, an A* search efficiently connects these explored zones to find the optimal path through the obstacles.
For over 40 years, finding the shortest path was dominated by Dijkstra's Algorithm. Its strategy is a meticulous "shock wave" that always finds the *absolute closest* unvisited node. This requires constantly sorting a large "frontier" of possibilities, creating a performance limit known as the "sorting bottleneck," a theoretical barrier thought to be unbreakable since the 1980s.
The 2025 breakthrough by Duan, Mao, et al. bypasses this by avoiding sorting altogether. It uses a divide-and-conquer strategy that works in layers. Instead of sorting every node, it groups the frontier into clusters and selects representative pivots. It then uses a few Bellman-Ford-style relaxations to propagate distances from these pivots. This approach is more efficient, though as the author of a proof-of-concept Rust implementation notes, you need "VERY large graphs under VERY specific circumstances" for it to outperform alternatives.
About These Simulations: These are conceptual visualizations (or "POCs" - Proof of Concepts) of these high-level strategies. The grid simulation shows a practical application on a maze, while the comparison below shows the core strategic differences on a classic graph problem.