1.7 KiB
1.7 KiB
Below are numbered block candidates for the topic "{topic}". They come from a similarity cluster. Some refer to the SAME block or a property of it, others are distinct. Group them.
CANDIDATES: {entries}
Rules:
- Form groups: numbers that belong to the SAME block go into ONE group.
- Watch the core entity (the problem/object): Clique, Vertex Cover, Set Cover, Knapsack, Dominating Set, LPT/List Scheduling … Different entity → different groups, even with similar phrasing ("Lower Bound Clique" ≠ "Lower Bound Vertex Cover").
- True paraphrases go TOGETHER, even when worded differently ("List Scheduling" = "LPT-Algorithmus"; "Set Cover" = "Mengenüberdeckung").
- A problem's properties belong TO the problem block — not on their own. Bundle with the problem: its complexity status (∈ NP, NP-schwer, NP-vollständig), its verifier / certificate / NDTM, "… als Sprache / Definition", its individual lower-bound parameters (k / r / |U|).
- Example: "Knapsack", "Knapsack ∈ NP", "Knapsack NP-schwer", "Knapsack NP-vollständig", "Verifizierer für Knapsack" → ONE group (the "Knapsack" block).
- Example: "Hitting Set Lower Bound (k)", "(r)", "(|U|)" → ONE group.
- Keep SEPARATE (own blocks): different problems (Clique-Member ≠ Clique-Nomember); a REDUCTION between two problems is its own technique (e.g. "3-SAT ⪯ k-Clique" stays separate); different methods/theorems with their own statement.
- When in doubt between two different problems → SEPARATE. For a problem + its property → BUNDLE.
- EVERY number goes into EXACTLY ONE group. A standalone block is a group with one element.
Write ONLY the JSON file to: {out_path}
Format (lists of candidate numbers; each number exactly once): {{"groups": 1, 3], [2], [4, 5}}