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Modifications of the Floyd-Warshall algorithm with nearly quadratic expected-time
Brodnik, Andrej ; Grgurovič, Marko ; Požar, Rok, 1986-
V članku sta opisani dve relativno preprosti spremembi dobro znanega Floyd-Warshallovega algoritma za izračun najkrajših poti med vsemi pari vozlišč. Bistvena razlika obeh sprememb v primerjavi s ...Floyd-Warshallovim algoritmom je v tem, da se sproščanje izvede na pameten način. Pokažemo, da je pričakovana časovna zahtevnost obeh algoritmov ▫$O(n^2\log^2 n)$▫ za razred polnih usmerjenih grafov na ▫$n$▫ vozliščih, pri čemer so uteži na povezavah izbrane neodvisno z vrednostmi enakomerno porazdeljene naključne spremenljivke na intervalu ▫$[0,1]$▫ Teoretično najboljši algoritmi za ta razred grafov temeljijo na Dijkstrovem algoritmu in dosežejo boljšo mejo v pričakovanem primeru. Kljub temu z empiričnim ovrednotenjem pokažemo, da sta naša algoritma v praksi vsaj konkurenčna z najbolj znanimi algoritmi in poleg tega prekašata večino od njih. Razlog za praktično učinkovitost predstavljenih algoritmov je odsotnost uporabe vrste s prednostjo.
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