Here is a problem I'm working on. Say you have a weighted, directed graph with n vertices and m edges, and you want to find the shortest path from s to all other vertices, *but* you can only use some ...

Most of you have used a navigation app like Google Maps for your travels at some point. These apps rely on algorithms that compute shortest paths through vast networks. Now imagine scaling that task ...

Fuzzy optimization for shortest path problems addresses uncertainty in network weights by representing arc costs with fuzzy numbers rather than crisp values. By extending classical algorithms—such as ...

The original version of this story appeared in Quanta Magazine. If you’ve been making the same commute for a long time, you’ve probably settled on what seems like the best route. But “best” is a ...