Historic algorithms help unlock shortest-path problem breakthrough

  • https://arxiv.org/abs/2203.03456 And https://arxiv.org/abs/2203.00671 Are the relevant papers

  • What’s an application where you’d absolutely have to have a graph with negative weights? Couldn’t you just preprocess the edges and normalize their weights?

  • What is meant by "nodes" in this article?

    > sum of the number of nodes and connections

    > Bellman-Ford instead needs many more steps: The total is based on the product of the number of nodes and vertices.

    > reduced the complexity to the square root of the number of vertices multiplied by the number of nodes

    At first I thought it was a synonym for vertices, in the same way the article inconsistently uses "connections" for edges. But then "nodes" gets used in the same breath as "vertices" in a way that contradicts that hypothesis.

  • This is precisely the sort of article where a bit of notation and interactive graphics would go far in presenting the information. Anyone who can understand this article knows big-O notation. It's silly to assume the article is more accessible just because it's in English.