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: Hitting Set problem | Statement: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, Hitting Set problem]

Target entity: Hitting Set problem
Context triple: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, Hitting Set problem]

• A. 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.
• B. Subset sum problem
  The subset sum problem is a classic NP-complete decision problem in computer science that asks whether any subset of given integers sums to a specified target value.
• C. Boolean satisfiability problem
  The Boolean satisfiability problem (SAT) is the canonical NP-complete decision problem of determining whether there exists an assignment of truth values to variables that makes a given Boolean formula evaluate to true.
• D. 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.
• E. Erdős–Ko–Rado theorem
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Hitting Set problem
Target entity description: The Hitting Set problem is a classic NP-complete combinatorial decision problem that asks whether there exists a small subset of elements that intersects every set in a given collection.

• A. 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.
• B. Subset sum problem
  The subset sum problem is a classic NP-complete decision problem in computer science that asks whether any subset of given integers sums to a specified target value.
• C. Boolean satisfiability problem
  The Boolean satisfiability problem (SAT) is the canonical NP-complete decision problem of determining whether there exists an assignment of truth values to variables that makes a given Boolean formula evaluate to true.
• D. 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.
• E. Erdős–Ko–Rado theorem
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• F. None of above. chosen