Triple
T13507145
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | union–find data structure |
E321042
|
entity |
| Predicate | usedInAlgorithm |
P25490
|
FINISHED |
| Object |
Kruskal’s minimum spanning tree algorithm
Kruskal’s minimum spanning tree algorithm is a classic greedy graph algorithm that builds a minimum spanning tree by repeatedly adding the smallest-weight edge that does not create a cycle, typically implemented efficiently using a union–find data structure.
|
E1045593
|
NE FINISHED |
How this triple was built (5 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Kruskal’s minimum spanning tree algorithm | Statement: [union–find data structure, usedInAlgorithm, Kruskal’s minimum spanning tree algorithm]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kruskal’s minimum spanning tree algorithm Context triple: [union–find data structure, usedInAlgorithm, Kruskal’s minimum spanning tree algorithm]
-
A.
Kruskal
Kruskal is a surname most prominently associated with American mathematician Martin David Kruskal, known for his work in soliton theory and nonlinear science.
-
B.
union–find data structure
The union–find data structure is an efficient algorithmic structure that maintains disjoint sets and supports fast union and find operations, widely used in graph algorithms such as Kruskal’s minimum spanning tree.
-
C.
Steiner tree problem
The Steiner tree problem is a classic optimization problem in combinatorial mathematics and computer science that seeks the shortest network of line segments connecting a given set of points, potentially adding extra intermediate points to minimize total length.
-
D.
Tarjan's strongly connected components algorithm
Tarjan's strongly connected components algorithm is a classic linear-time graph algorithm that efficiently identifies all strongly connected components in a directed graph using depth-first search and low-link values.
-
E.
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.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Kruskal’s minimum spanning tree algorithm Triple: [union–find data structure, usedInAlgorithm, Kruskal’s minimum spanning tree algorithm]
Generated description
Kruskal’s minimum spanning tree algorithm is a classic greedy graph algorithm that builds a minimum spanning tree by repeatedly adding the smallest-weight edge that does not create a cycle, typically implemented efficiently using a union–find data structure.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kruskal’s minimum spanning tree algorithm Target entity description: Kruskal’s minimum spanning tree algorithm is a classic greedy graph algorithm that builds a minimum spanning tree by repeatedly adding the smallest-weight edge that does not create a cycle, typically implemented efficiently using a union–find data structure.
-
A.
Kruskal
Kruskal is a surname most prominently associated with American mathematician Martin David Kruskal, known for his work in soliton theory and nonlinear science.
-
B.
union–find data structure
The union–find data structure is an efficient algorithmic structure that maintains disjoint sets and supports fast union and find operations, widely used in graph algorithms such as Kruskal’s minimum spanning tree.
-
C.
Steiner tree problem
The Steiner tree problem is a classic optimization problem in combinatorial mathematics and computer science that seeks the shortest network of line segments connecting a given set of points, potentially adding extra intermediate points to minimize total length.
-
D.
Tarjan's strongly connected components algorithm
Tarjan's strongly connected components algorithm is a classic linear-time graph algorithm that efficiently identifies all strongly connected components in a directed graph using depth-first search and low-link values.
-
E.
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.
- F. None of above. chosen
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: usedInAlgorithm Context triple: [union–find data structure, usedInAlgorithm, Kruskal’s minimum spanning tree algorithm]
-
A.
usedInMethod
Indicates that something (such as a component, variable, or resource) is utilized or referenced within the execution or implementation of a particular method.
-
B.
usedInOperation
Indicates that something (such as a tool, method, or resource) is employed or applied during the execution of a particular operation or procedure.
-
C.
usedInArgumentFor
Indicates that something (such as a statement, piece of evidence, or concept) is employed as support within an argument advocating for a particular claim or position.
-
D.
usedInType
Indicates that something serves as a component, element, or example within a particular type or category.
-
E.
areUsedIn
chosen
Indicates that certain entities serve as components, tools, or resources within a particular process, context, or application.
- F. None of above.
Provenance (6 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69d807629d6c8190998f1b9bb12d2ed0 |
completed | April 9, 2026, 8:09 p.m. |
| NER | Named-entity recognition | batch_69dbaf8259a08190ada13c4a3078f07d |
completed | April 12, 2026, 2:43 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f7548e51b881909a3384812556bc3d |
completed | May 3, 2026, 1:58 p.m. |
| NEDg | Description generation | batch_69f757108e088190aeec031eccc9aca3 |
completed | May 3, 2026, 2:09 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69f757e7322c8190b0e36e8373d42ac4 |
completed | May 3, 2026, 2:12 p.m. |
| PD | Predicate disambiguation | batch_69dbae0b63748190b5e207f84b2532ea |
completed | April 12, 2026, 2:36 p.m. |
Created at: April 9, 2026, 9:43 p.m.