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 ...

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 ...