Refining with colors Mathematicians have developed various strategies to compare graphs. Since the 1970s, algorithms have been able to test graph isomorphism, but in exponential time.

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 paper considers a project scheduling problem in weighted directed graphs in which arcs represent operations while nodes are identified with starting and finishing endpoints of the operations; arc ...