在非常大规模的加权和有向图中获得所有对最短路径的最佳方法是什么？

Question

I'm trying to find all pair shortest path in very large scale graph. I tried floyd-warshall but it is not fast enough because of very large scale of the graph. Number of vertices is more than 100k. Maybe it will take more than a week... Actually I don't need all of the paths. I only need the longest one.

Answer 1

You might want to implement the all-pair-shortest-path variant of Hagerup . The time bound of O(nm + n^2 log log n) might be much better than Floyd–Warshalls O(n^3) depending on how many edges your graphs have.

You might also be able to set up Neo4j and use it to calculate that path: https://neo4j.com/docs/graph-data-science/current/alpha-algorithms/all-pairs-shortest-path/#algorithm-all-pairs-shortest-path-sample

CALL gds.alpha.allShortestPaths.stream({
  nodeProjection: 'Loc',
  relationshipProjection: {
    ROAD: {
      type: 'ROAD',
      properties: 'cost'
    }
  },
  relationshipWeightProperty: 'cost'
})

I don't know that, but depending on the syntax you might be able to select only specific paths from the stream.