Triple

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).

Phrase: 3-Dimensional Matching problem | Statement: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, 3-Dimensional Matching problem]

Target entity: 3-Dimensional Matching problem
Context triple: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, 3-Dimensional Matching problem]

• A. 3-SAT
  3-SAT is a classic Boolean satisfiability problem where each clause has exactly three literals and which serves as a fundamental NP-complete benchmark in computational complexity theory.
• B. Clique problem
  The Clique problem is a classic NP-complete decision problem in graph theory that asks whether a graph contains a fully connected subgraph (clique) of at least a given size.
• C. Max-3-SAT
  Max-3-SAT is an optimization variant of the Boolean satisfiability problem where the goal is to maximize the number of satisfied clauses, each containing exactly three literals, and it serves as a central problem in the study of approximation algorithms and hardness of approximation.
• D. A Combinatorial Problem
  "A Combinatorial Problem" is a classic mathematical paper by N. G. de Bruijn that introduces and analyzes a fundamental counting problem in combinatorics.
• E. Happy Ending problem
  The Happy Ending problem is a famous combinatorial geometry question that investigates the minimum number of points in general position in the plane needed to guarantee the existence of a convex polygon with a given number of vertices.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: 3-Dimensional Matching problem
Target entity description: The 3-Dimensional Matching problem is a classic NP-complete combinatorial decision problem that asks whether there exists a perfect matching selecting disjoint triples from three equally sized sets.

• A. 3-SAT
  3-SAT is a classic Boolean satisfiability problem where each clause has exactly three literals and which serves as a fundamental NP-complete benchmark in computational complexity theory.
• B. Clique problem
  The Clique problem is a classic NP-complete decision problem in graph theory that asks whether a graph contains a fully connected subgraph (clique) of at least a given size.
• C. Max-3-SAT
  Max-3-SAT is an optimization variant of the Boolean satisfiability problem where the goal is to maximize the number of satisfied clauses, each containing exactly three literals, and it serves as a central problem in the study of approximation algorithms and hardness of approximation.
• D. A Combinatorial Problem
  "A Combinatorial Problem" is a classic mathematical paper by N. G. de Bruijn that introduces and analyzes a fundamental counting problem in combinatorics.
• E. Happy Ending problem
  The Happy Ending problem is a famous combinatorial geometry question that investigates the minimum number of points in general position in the plane needed to guarantee the existence of a convex polygon with a given number of vertices.
• F. None of above. chosen