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: Steiner Tree problem (decision version) | Statement: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, Steiner Tree problem (decision version)]

Target entity: Steiner Tree problem (decision version)
Context triple: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, Steiner Tree problem (decision version)]

• 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. Kruskal’s minimum spanning tree algorithm
  Kruskal’s minimum spanning tree algorithm is a classic greedy graph algorithm that builds a minimum spanning tree by repeatedly adding the smallest-weight edge that does not create a cycle, typically implemented efficiently using a union–find data structure.
• C. 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.
• D. Menger theorem in graph theory
  Menger's theorem in graph theory is a fundamental result that characterizes the connectivity between two vertices in a graph by equating the maximum number of pairwise internally disjoint paths between them with the minimum size of a vertex cut separating them.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.