Went greedy pretty fast, felt good about it in the moment.
Start by clarifying the problem constraints and defining what 'balanced' means (e.g., each (model, question) pair appears roughly equally often, and each annotator sees a similar distribution of models). Then propose a two-phase algorithm: first generate a balanced list of (model, question) pairs, then assign annotators to these pairs in a round-robin or greedy manner to balance model exposure per annotator. Discuss trade-offs like randomness vs determinism and scalability.
Pro tip: Mention that perfect balance may be impossible due to indivisibility, so aim for near-balance and consider using a randomized algorithm with a seed for reproducibility. Also, highlight the importance of monitoring and adjusting in production.
Ask questions to understand the scale (number of annotators, models, questions), whether each annotator must see each question at most once, and if there are any constraints on model exposure per annotator. Define 'balanced' precisely.
Create a list where each (model, question) pair appears as evenly as possible. If total pairs T = M * Q, and we need N tuples, distribute the N occurrences across T pairs such that counts differ by at most 1. Use a round-robin or cyclic distribution.
Assign annotators to the generated (model, question) pairs such that each annotator sees a balanced distribution of models. Use a greedy approach: for each annotator, assign pairs with models they've seen least, ensuring overall balance.
Discuss time/space complexity, potential need for randomization to avoid bias, and how the algorithm scales with large numbers. Mention alternative approaches like integer linear programming for optimal balance.
Propose test cases (e.g., small numbers, uneven counts) to verify balance. Suggest metrics to measure balance (e.g., max-min difference in counts) and how to handle edge cases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.