A new proof shows that an upgraded version of the 70-year-old Dijkstra’s algorithm reigns supreme: It finds the most efficient pathways through any graph.

It doesn’t just tell you the fastest route to one destination.

In an interview toward the end of his life, Dijkstra credited his algorithm’s enduring appeal in part to its unusual origin story. “Without pencil and paper you are almost forced to avoid all avoidable complexities,” he said.

Dijkstra’s algorithm doesn’t just tell you the fastest route to one destination. Instead, it gives you an ordered list of travel times from your current location to every other point that you might want to visit — a solution to what researchers call the single-source shortest-paths problem. The algorithm works in an abstracted road map called a graph: a network of interconnected points (called vertices) in which the links between vertices are labeled with numbers (called weights). These weights might represent the time required to traverse each road in a network, and they can change depending on traffic patterns. The larger a weight, the longer it takes to traverse that path.