Editing Floyd–Warshall algorithm (section)

==History and naming==
The Floyd–Warshall algorithm is an example of [[dynamic programming]], and was published in its currently recognized form by [[Robert W. Floyd|Robert Floyd]] in 1962.<ref>{{cite journal | first = Robert W. | last = Floyd | author-link = Robert W. Floyd | title = Algorithm 97: Shortest Path | journal = [[Communications of the ACM]] | volume = 5 | issue = 6 | page = 345 | date=  June 1962 | doi = 10.1145/367766.368168 | s2cid = 2003382 | doi-access = free }}</ref>  However, it is essentially the same as algorithms previously published by [[Bernard Roy]] in 1959<ref>{{cite journal | first = Bernard | last = Roy |author-link=Bernard Roy| title = Transitivité et connexité. | journal = [[C. R. Acad. Sci. Paris]] | volume = 249 | pages = 216–218 | year=  1959 |url=https://gallica.bnf.fr/ark:/12148/bpt6k3201c/f222.image |language=fr }}
</ref> and also by [[Stephen Warshall]] in 1962<ref>{{cite journal | first = Stephen | last = Warshall | title = A theorem on Boolean matrices | journal = [[Journal of the ACM]] | volume = 9 | issue = 1 | pages = 11–12 | date=  January 1962 | doi = 10.1145/321105.321107 | s2cid = 33763989 | doi-access = free }}</ref> for finding the transitive closure of a graph,<ref>{{mathworld|id=Floyd-WarshallAlgorithm | title = Floyd-Warshall Algorithm}}</ref> and is closely related to [[Kleene's algorithm]] (published in 1956) for converting a [[deterministic finite automaton]] into a [[regular expression]], with the difference being the use of a min-plus [[semiring]].<ref>{{cite book | author-link = Stephen Cole Kleene | first = S. C. | last = Kleene | chapter = Representation of events in nerve nets and finite automata | title = Automata Studies | editor = [[Claude Elwood Shannon|C. E. Shannon]] and [[John McCarthy (computer scientist)|J. McCarthy]] | pages = 3–42 | publisher = Princeton University Press | year=  1956 }}</ref> The modern formulation of the algorithm as three nested for-loops was first described by Peter Ingerman, also in 1962.<ref>{{cite journal | first = Peter Z. | last = Ingerman | title = Algorithm 141: Path Matrix | journal = [[Communications of the ACM]] | volume = 5 | number = 11 | page = 556 | date = November 1962 | doi = 10.1145/368996.369016 | s2cid = 29010500 | doi-access = free }}</ref>