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.