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.

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.

The problem is to find the earliest starting times for all operations. This problem generalizes the shortest path problem and the critical path problem. The complexity of the suggested algorithm is O ...