Complexity Analysis and Performance Modeling Questions

Analyze algorithmic and system complexity including time and space complexity in asymptotic terms and real world performance modeling. Candidates should be fluent with Big O, Big Theta, and Big Omega notation and common complexity classes, and able to reason about average case versus worst case and trade offs between different algorithmic approaches. Extend algorithmic analysis into system performance considerations: estimate execution time, memory usage, I O and network costs, cache behavior, instruction and cycle counts, and power or latency budgets. Include methods for profiling, benchmarking, modeling throughput and latency, and translating asymptotic complexity into practical performance expectations for real systems.

HardSystem Design

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Design a performance and bandwidth model for a federated learning setup with M clients, local update size U bytes per round, R communication rounds, and fraction p of clients participating per round. Include heterogenous client connectivity (varying bandwidths and latency), partial participation, and techniques like update compression and secure aggregation. Estimate total bytes transferred and expected wall-clock time for a single federated round.

HardTechnical

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Given checkpoint cost C seconds and a mean time between failures (MTBF) of T seconds (for example due to spot interruptions), derive the checkpoint interval that minimizes expected wasted work using the Young/Daly model. Extend the model to include restore time R and checkpoint storage costs, and explain how the optimal interval changes in a distributed multi-worker training setup.

HardTechnical

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You deploy a new model version and observe a 30% slowdown in p95 inference latency across the fleet. Outline a systematic debugging plan to isolate the root cause across model changes, runtime or driver updates, hardware differences, dependency upgrades, and infra changes. List the metrics, traces, and binary-search rollback steps you would execute and quick mitigations to restore SLA.

MediumTechnical

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How would you instrument and visualize GPU memory usage across a large multi-worker training run to detect memory leaks or fragmentation? Describe the data-collection method (NVML/Nvidia-smi, periodic dumps), visualization approach (time series per worker and aggregated HWM), and what patterns indicate true leaks versus expected episodic growth (e.g., gradient accumulation).

MediumTechnical

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When benchmarking model performance across cloud providers and instance types, what steps ensure reproducibility and fairness? Cover environment capture (software/hardware), microbenchmarking, isolating noisy neighbors, running multiple trials for statistical significance, and CI-friendly benchmarking approaches with example metrics to save.

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