Bellman–Ford algorithm
E880220
The Bellman–Ford algorithm is a graph shortest-path algorithm that can handle negative edge weights and detect negative cycles, often used in routing and network optimization.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Bellman–Ford algorithm canonical | 3 |
| Bellman-Ford algorithm | 2 |
| Bellman-Ford-Moore algorithm | 1 |
| Johnson's algorithm | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10700882 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bellman–Ford algorithm Context triple: [Viterbi algorithm, relatedTo, Bellman–Ford algorithm]
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A.
Dijkstra
Dijkstra is a renowned Dutch computer scientist best known for his pioneering work in algorithms, including Dijkstra's shortest path algorithm, and for his influential contributions to programming methodology and software engineering.
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B.
Cristian's algorithm
Cristian's algorithm is a clock synchronization method in distributed systems that estimates accurate time on client machines by querying a time server and adjusting for message delays.
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C.
Bellman
Bellman is a surname most prominently associated with New Zealand-born British actress Gina Bellman, known for her roles in television and film.
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D.
Kruskal
Kruskal is a surname most prominently associated with American mathematician Martin David Kruskal, known for his work in soliton theory and nonlinear science.
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E.
Viterbi algorithm
The Viterbi algorithm is a dynamic programming method used to find the most likely sequence of hidden states in probabilistic models such as Hidden Markov Models, widely applied in fields like digital communications, speech recognition, and bioinformatics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bellman–Ford algorithm Target entity description: The Bellman–Ford algorithm is a graph shortest-path algorithm that can handle negative edge weights and detect negative cycles, often used in routing and network optimization.
-
A.
Dijkstra
Dijkstra is a renowned Dutch computer scientist best known for his pioneering work in algorithms, including Dijkstra's shortest path algorithm, and for his influential contributions to programming methodology and software engineering.
-
B.
Cristian's algorithm
Cristian's algorithm is a clock synchronization method in distributed systems that estimates accurate time on client machines by querying a time server and adjusting for message delays.
-
C.
Bellman
Bellman is a surname most prominently associated with New Zealand-born British actress Gina Bellman, known for her roles in television and film.
-
D.
Kruskal
Kruskal is a surname most prominently associated with American mathematician Martin David Kruskal, known for his work in soliton theory and nonlinear science.
-
E.
Viterbi algorithm
The Viterbi algorithm is a dynamic programming method used to find the most likely sequence of hidden states in probabilistic models such as Hidden Markov Models, widely applied in fields like digital communications, speech recognition, and bioinformatics.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
graph algorithm
ⓘ
shortest path algorithm ⓘ single-source shortest path algorithm ⓘ |
| advantageOver | Dijkstra's algorithm with respect to negative weights ⓘ |
| alsoKnownAs |
Bellman-Ford-Moore algorithm
ⓘ
linked to:
Bellman–Ford algorithm
|
| assumes | no overflow in distance calculations ⓘ |
| basedOn | dynamic programming ⓘ |
| canBeOptimizedBy | early stopping when no updates occur ⓘ |
| canDetect | negative weight cycles reachable from source ⓘ |
| canHandle | negative edge weights ⓘ |
| category |
combinatorial optimization
ⓘ
computer science algorithm ⓘ graph theory ⓘ |
| comparedWith |
Dijkstra's algorithm
ⓘ
linked to:
Dijkstra's shortest path algorithm
|
| coreOperation | edge relaxation ⓘ |
| detectionMethodForNegativeCycles | extra relaxation pass that finds further distance decreases ⓘ |
| disadvantageComparedTo | Dijkstra's algorithm in time complexity on non-negative graphs ⓘ |
| failsWhen | negative cycle is present and distances are considered finite ⓘ |
| generalizes | shortest paths in presence of negative edges ⓘ |
| input |
graph with edge weights
ⓘ
single source vertex ⓘ |
| namedAfter |
Lester R. Ford Jr.
ⓘ
Richard Bellman ⓘ
linked to:
Richard E. Bellman
|
| notSuitableFor | graphs with negative cycles when finite shortest paths are required ⓘ |
| numberOfRelaxationPasses | |V| - 1 ⓘ |
| operatesOn |
weighted directed graph
ⓘ
weighted undirected graph ⓘ |
| originalAuthor |
Lester R. Ford Jr.
ⓘ
Richard Bellman ⓘ
linked to:
Richard E. Bellman
|
| originallyPublishedIn | 1950s ⓘ |
| output | shortest path distances from source to all vertices ⓘ |
| relatedConcept |
distance-vector algorithm
ⓘ
shortest path problem ⓘ |
| requiresEdgeWeightsToBe | finite ⓘ |
| spaceComplexity | O(V) ⓘ |
| terminationCondition | no distance updated in a full pass or after |V|-1 passes ⓘ |
| timeComplexityTypical | O(V * E) ⓘ |
| timeComplexityWorstCase | O(V * E) ⓘ |
| typicalInitialization |
distance to all other vertices is infinity
ⓘ
distance to source is 0 ⓘ |
| usedAsSubroutineIn | Johnson's algorithm for all-pairs shortest paths ⓘ |
| usedFor | feasibility check of potentials in reweighting schemes ⓘ |
| usedIn |
distance-vector routing
ⓘ
distributed routing algorithms ⓘ dynamic programming teaching ⓘ network optimization ⓘ routing protocols ⓘ |
| worksWith |
directed graphs
ⓘ
undirected graphs modeled as bidirected ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Bellman–Ford algorithm Description of subject: The Bellman–Ford algorithm is a graph shortest-path algorithm that can handle negative edge weights and detect negative cycles, often used in routing and network optimization.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Bellman–Ford algorithm
linked to: Bellman–Ford algorithm
linked to: Bellman–Ford algorithm
linked to: Bellman–Ford algorithm