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Floyd–Warshall algorithm

In computer science, the Floyd–Warshall algorithm (also known as Floyd's algorithm, the Roy–Warshall algorithm, the Roy–Floyd algorithm, or the WFI algorithm) is an algorithm for finding shortest paths in a directed weighted graph with positive or negative edge weights (but with no negative cycles). A single execution of the algorithm will find the…

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Average performance
Θ ( | V | 3 ) {\displaystyle \Theta (|V|^{3})}
Best-case performance
Θ ( | V | 3 ) {\displaystyle \Theta (|V|^{3})}
Class
All-pairs shortest path problem (for weighted graphs)
Data structure
Graph
Worst-case performance
Θ ( | V | 3 ) {\displaystyle \Theta (|V|^{3})}
Worst-case space complexity
Θ ( | V | 2 ) {\displaystyle \Theta (|V|^{2})}

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Overview

History and naming

Algorithm

Behavior with negative cycles

Path reconstruction

Time complexity

Applications and generalizations

Implementations

Comparison with other shortest path algorithms

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Floyd–Warshall algorithm

Nodes59
Edges58
Triples76
Avg. degree1.97
Density0.033898
Components1

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Floyd–Warshall algorithm

Top relations

has application · 27
Floyd–Warshall algorithm → AND, AND/OR/threshold, Boolean, Computing, DBMs, Fast, Finding, Floyd, Gauss, In, In Warshall's, Inversion, Jordan, Kleene's, Maximum, Optimal, OR, Path, Pathfinder, The
related to Behavior with negative cycles · 9
Floyd–Warshall algorithm → Floyd, For, Initially, Nevertheless, The, The Floyd, There, Thus, Warshall
related to history · 9
Floyd–Warshall algorithm → Bernard Roy, However, Kleene's, Peter Ingerman, Robert Floyd, Stephen Warshall, The, The Floyd, Warshall
related to Algorithm · 8
Floyd–Warshall algorithm → By, Consider, Further, It, Now, The Floyd, Theta, Warshall
related to Path reconstruction · 6
Floyd–Warshall algorithm → Instead, The Floyd, Theta, Warshall, While, With
related to External links · 5
Floyd–Warshall algorithm → Floyd, Interactive, Munich, Technical University, Warshall
related to Pseudocode · 5
Floyd–Warshall algorithm → Floyd, However, Note, The, Warshall
Average performance · 1
Floyd–Warshall algorithm → Θ ( | V | 3 ) {\displaystyle \Theta (|V|^{3})}
Best-case performance · 1
Floyd–Warshall algorithm → Θ ( | V | 3 ) {\displaystyle \Theta (|V|^{3})}
Class · 1
Floyd–Warshall algorithm → All-pairs shortest path problem (for weighted graphs)

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Important terminology

algorithm displaystyle path graph vertices paths shortest warshall floyd negative cycles time using vertex weights pairs graphs theta mathrm shortestpath

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Floyd–Warshall algorithmAverage performanceΘ ( | V | 3 ) {\displaystyle \Theta (|V|^{3})}1.00infobox
Floyd–Warshall algorithmBest-case performanceΘ ( | V | 3 ) {\displaystyle \Theta (|V|^{3})}1.00infobox
Floyd–Warshall algorithmClassAll-pairs shortest path problem (for weighted graphs)1.00infobox
Floyd–Warshall algorithmData structureGraph1.00infobox
Floyd–Warshall algorithmWorst-case performanceΘ ( | V | 3 ) {\displaystyle \Theta (|V|^{3})}1.00infobox
Floyd–Warshall algorithmWorst-case space complexityΘ ( | V | 2 ) {\displaystyle \Theta (|V|^{2})}1.00infobox
Floyd–Warshall algorithmis aexample of dynamic programming0.90text
Floyd–Warshall algorithmhas applicationThe Floyd0.60section
Floyd–Warshall algorithmhas applicationWarshall0.60section
Floyd–Warshall algorithmhas applicationTransitive0.60section
Floyd–Warshall algorithmhas applicationWarshall's0.60section
Floyd–Warshall algorithmhas applicationIn Warshall's0.60section

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