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Bellman–Ford algorithm

The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers. The algorithm was first…

Applications, Secondary sources & Applications in routing

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Best-case performance
Θ ( | E | ) {\displaystyle \Theta (|E|)}
Class
Single-source shortest path problem (for weighted directed graphs)
Data structure
Graph
Worst-case performance
Θ ( | V | | E | ) {\displaystyle \Theta (|V||E|)}
Worst-case space complexity
Θ ( | V | ) {\displaystyle \Theta (|V|)}

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Overview

Algorithm

Proof of correctness

Finding negative cycles

Applications in routing

Improvements

Original sources

Secondary sources

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Bellman–Ford algorithm

Nodes52
Edges51
Triples168
Avg. degree1.96
Density0.038462
Components1

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Bellman–Ford algorithm

Top relations

related to Original sources · 66
Bellman–Ford algorithm → An, ANALCO12, Analytic Algorithmics, Annual ACM Symposium, Applied Mathematics, Association, August, Bannister, BC, Bellman, Bojan, Brooklyn, California, Cambridge, Canada, Combinatorics, Computing, Computing Machinery, Edward, Eppstein
related to Secondary sources · 63
Bellman–Ford algorithm → Addison-Wesley, Alexander, Algorithm Design, Algorithms, Applications, Archived, Bang-Jensen, Chapter, Charles, Clifford, Cormen, Digraphs, Discrete Optimization, Elsevier, First, Flows, Ford, Fulkerson, Gary, George
has application · 12
Bellman–Ford algorithm → AS, Autonomous, Bellman, Each, Ford, IP, ISP, It, RIP, Routing Information Protocol, The, When
related to Improvements · 11
Bellman–Ford algorithm → Bellman, Fanding Duan, Ford, If, In, In China, Moore, The, The Bellman, This, With
related to Algorithm · 6
Bellman–Ford algorithm → Bellman, Dijkstra's, Ford, However, In, Like Dijkstra's
related to Finding negative cycles · 4
Bellman–Ford algorithm → Bellman, Ford, However, When
Best-case performance · 1
Bellman–Ford algorithm → Θ ( | E | ) {\displaystyle \Theta (|E|)}
Class · 1
Bellman–Ford algorithm → Single-source shortest path problem (for weighted directed graphs)
Data structure · 1
Bellman–Ford algorithm → Graph
Worst-case performance · 1
Bellman–Ford algorithm → Θ ( | V | | E | ) {\displaystyle \Theta (|V||E|)}

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Important terminology

algorithm path edges ford bellman shortest negative distance source vertex displaystyle cycle vertices length edge time number nodes loop first

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Bellman–Ford algorithmBest-case performanceΘ ( | E | ) {\displaystyle \Theta (|E|)}1.00infobox
Bellman–Ford algorithmClassSingle-source shortest path problem (for weighted directed graphs)1.00infobox
Bellman–Ford algorithmData structureGraph1.00infobox
Bellman–Ford algorithmWorst-case performanceΘ ( | V | | E | ) {\displaystyle \Theta (|V||E|)}1.00infobox
Bellman–Ford algorithmWorst-case space complexityΘ ( | V | ) {\displaystyle \Theta (|V|)}1.00infobox
Bellman–Ford algorithmis aalgorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph0.90text
Bellman–Ford algorithmhas applicationBellman0.60section
Bellman–Ford algorithmhas applicationFord0.60section
Bellman–Ford algorithmhas applicationRouting Information Protocol0.60section
Bellman–Ford algorithmhas applicationRIP0.60section
Bellman–Ford algorithmhas applicationThe0.60section
Bellman–Ford algorithmhas applicationAutonomous0.60section

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