In such cases, the fastest known shortest-path algorithm doesn’t work. For decades, fast algorithms for finding shortest paths on negative-weight graphs have remained elusive.

A canonical problem in computer science is to find the shortest route to every point in a network. A new approach beats the classic algorithm taught in textbooks.

One of the most classic algorithmic problems deals with calculating the shortest path between two points. A more complicated variant of the problem is when the route traverses a changing network ...