In algorithms, as in life, negativity can be a drag. Consider the problem of finding the shortest path between two points on a graph — a network of nodes connected by links, or edges. Often, these ...

Graph algorithms constitute a pivotal component of modern computational science, underpinning diverse applications ranging from transportation optimisation and telecommunications to social network ...

The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...

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 ...

* Why do you want to base this on Dijkstra's algorithm, which is designed to find a single shortest-path? Surely there are better options for your base implementation. A quick Google search suggests a ...

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 slippery concept. Perhaps one day there’s an accident or road closure ...