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.

EasyTechnical

64 practiced

Describe average-case versus worst-case complexity. For quicksort (with common pivot strategies) and hash table lookup, explain what input or adversarial scenarios produce average versus worst-case behavior. Discuss how input distributions and implementation choices (e.g., pivot selection, hash function) affect measured runtime in practice and when average-case analysis is more appropriate for system design.

MediumTechnical

67 practiced

Explain how RDMA (e.g., InfiniBand) changes performance characteristics for distributed training compared to TCP over Ethernet. Discuss latency, CPU overhead, bandwidth utilization, and implications for collective algorithms (e.g., all-reduce). Provide specifics on when RDMA makes the most difference for scaling.

HardSystem Design

63 practiced

Design a serving architecture for a generative text API that must handle 500 requests/second with median latency < 100ms and p99 < 500ms under cost constraints. Consider batching strategies, GPU sharing, RPC and serialization overhead, model warm vs cold containers, and admission control. Provide a performance model estimating required GPUs, acceptable batch sizes, and trade-offs between batching and tail latency.

MediumTechnical

63 practiced

Compare Amdahl's Law and Gustafson's Law for parallel scalability. If 70% of a training job is perfectly parallelizable, compute theoretical speedup on 8 GPUs using both laws. Explain which law is more realistic for strong scaling vs weak scaling in machine learning workloads and why.

MediumTechnical

90 practiced

Build a cost model comparing training a large model on a single high-end p4d instance versus distributing across many smaller GPU instances (including spot instances). Include compute hours, expected wall-clock training time given scaling efficiency, network egress/ingress costs, checkpoint storage and restore costs, and the expected loss from spot preemption. State assumptions and sensitivity to spot termination rates.

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