Triple

T21494602
Position Surface form Disambiguated ID Type / Status
Subject Steiner tree problem E530318 entity
Predicate hasSpecialCase P7025 FINISHED
Object Steiner tree in series-parallel graphs — NE NERFINISHED

How this triple was built (2 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: Steiner tree in series-parallel graphs | Statement: [Steiner tree problem, hasSpecialCase, Steiner tree in series-parallel graphs]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Steiner tree in series-parallel graphs
Context triple: [Steiner tree problem, hasSpecialCase, Steiner tree in series-parallel graphs]
  • A. Steiner tree problem chosen
    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.
  • B. Lipton–Tarjan separator theorem
    The Lipton–Tarjan separator theorem is a fundamental result in graph theory that shows any planar graph can be efficiently divided into roughly equal parts by removing only a relatively small set of vertices, enabling faster algorithms for many computational problems.
  • C. Gale’s theorem on flows with convex costs
    Gale’s theorem on flows with convex costs is a fundamental result in mathematical optimization and network flow theory that characterizes optimal flows in networks when the cost functions on edges are convex rather than linear.
  • D. Combinatorial Optimization: Algorithms and Complexity
    Combinatorial Optimization: Algorithms and Complexity is a foundational textbook that systematically develops the theory and algorithms of combinatorial optimization, emphasizing computational complexity and algorithmic efficiency.
  • E. Graph Algorithms (book)
    "Graph Algorithms" is a foundational textbook by Shimon Even that systematically presents the theory, design, and analysis of algorithms for solving fundamental problems on graphs.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e0c45bd15481909fba5910765cdda2 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69e9ea567244819091863350fedae3ae completed April 23, 2026, 9:45 a.m.
Created at: April 16, 2026, 6:23 p.m.