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

Target entity: Feedback Vertex Set problem
Context triple: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, Feedback Vertex 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. 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.
• C. Papadimitriou–Yannakakis theorem
  The Papadimitriou–Yannakakis theorem is a fundamental result in computational complexity theory that characterizes the complexity of certain optimization and approximation problems, particularly in relation to classes like NP and the theory of approximation algorithms.
• 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. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Feedback Vertex Set problem
Target entity description: The Feedback Vertex Set problem is a classic NP-complete graph-theoretic decision problem that asks whether a given graph contains a set of vertices whose removal makes it acyclic.

• 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. 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.
• C. Papadimitriou–Yannakakis theorem
  The Papadimitriou–Yannakakis theorem is a fundamental result in computational complexity theory that characterizes the complexity of certain optimization and approximation problems, particularly in relation to classes like NP and the theory of approximation algorithms.
• 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. 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.
• F. None of above. chosen