Floyd-Warshall: Unearthing All-Pairs Shortest Paths

The All-Pairs Shortest Path Problem (APSP)

The All-Pairs Shortest Path Problem (APSP) is a fundamental challenge in graph theory: given a weighted graph, find the shortest path between every possible pair of vertices. While Dijkstra's algorithm or Bellman-Ford can be applied repeatedly from each vertex, this approach can be computationally expensive, especially for dense graphs. Enter the Floyd-Warshall algorithm, a dynamic programming solution that elegantly addresses this by systematically considering intermediate vertices.