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: Max-Cut | Statement: [Max-E3-LIN-2, relatedProblem, Max-Cut]

Target entity: Max-Cut
Context triple: [Max-E3-LIN-2, relatedProblem, Max-Cut]

• 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. 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. Max-SAT
  Max-SAT is the optimization variant of the Boolean satisfiability problem in which the goal is to find an assignment that satisfies the maximum possible number of clauses, making it a central problem in approximation algorithms and complexity theory.
• E. Steiner forest problem
  The Steiner forest problem is a combinatorial optimization problem that seeks a minimum-cost forest connecting specified pairs or groups of terminals in a graph, generalizing the classical Steiner tree problem to multiple disjoint terminal sets.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Max-Cut
Target entity description: Max-Cut is a fundamental NP-hard problem in graph theory and combinatorial optimization that seeks a partition of a graph’s vertices into two sets to maximize the number (or total weight) of edges crossing between them.

• 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. 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. Max-SAT
  Max-SAT is the optimization variant of the Boolean satisfiability problem in which the goal is to find an assignment that satisfies the maximum possible number of clauses, making it a central problem in approximation algorithms and complexity theory.
• E. Steiner forest problem
  The Steiner forest problem is a combinatorial optimization problem that seeks a minimum-cost forest connecting specified pairs or groups of terminals in a graph, generalizing the classical Steiner tree problem to multiple disjoint terminal sets.
• F. None of above. chosen