The part that tripped me up was that 'minimize imbalance' and 'minimize moves' pull in opposite directions and you can't fully satisfy both.
Start by clarifying the problem: define load, constraints, and objectives (minimize imbalance and moves). Then propose a two-phase algorithm: first compute a target balanced assignment, then use a cost-aware matching or local search to move shards with minimal disruption. Discuss trade-offs and how to tune parameters based on system priorities.
Pro tip: Emphasize that perfect balance is often not worth the move cost; propose a threshold-based approach where you only rebalance when imbalance exceeds a certain percentage, and use incremental moves to avoid thrashing.
Ask questions to understand what 'load' means (CPU, memory, QPS), whether shards can be split, if there are hard constraints (e.g., rack awareness), and the acceptable trade-off between balance and moves.
Formalize the objective function: minimize a weighted sum of imbalance (e.g., standard deviation of node loads) and number of shard moves. Define imbalance metric and move cost.
Propose a two-phase approach: (1) compute a target balanced assignment using a greedy or optimization method (e.g., bin packing, linear programming), (2) find a minimal set of moves to reach that target using a matching algorithm or local search (e.g., min-cost max-flow, simulated annealing).
Discuss time/space complexity, scalability, and how the algorithm behaves under different scenarios (e.g., homogeneous vs heterogeneous nodes). Explain how to tune parameters to prioritize balance vs move cost.
Address incremental rebalancing, avoiding oscillations, handling node failures, and ensuring the algorithm is online and safe (e.g., move shards in batches with throttling).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.