A Very General Method of Computing Shortest Paths (and much more)

Quoting from there: “I would like to introduce you to a very general algorithm that I like to call the Gauss-Jordan-Floyd-Warshall-Kleene algorithm. With this simple algorithm (an algorithm whose implementation is not very much longer than its name) you can solve almost half of the problems you might encounter in computer science. For instance, this algorithm will let you:

• compute transitive closures
• compute shortest paths
• compute largest capacity paths
• compute most reliable paths
• compute the regular expression for a finite automaton
• solve linear equations”