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.

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Estimate the RAM required to load a dataset of 12,000,000 samples where each sample has 300 float32 features and a 1-byte label. Show the raw data calculation and then include commonly overlooked overheads: numpy array metadata, Python object overhead if stored as a list of lists, and additional memory needed during training for Adam optimizer (assume Adam keeps two additional float32 tensors per parameter).

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Analyze BFS complexity. For a graph with V vertices and E edges, derive time and space complexity for BFS when the graph is represented using (a) adjacency lists and (b) an adjacency matrix. For ML use cases such as knowledge graphs (sparse graphs), which representation would you choose and why? Also discuss cache/locality effects and memory layout choices that could affect real-world performance.

MediumTechnical

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You have a neural network with 100 million parameters. Estimate GPU memory usage during training for batch size 32 using float32 parameters and the Adam optimizer (assume Adam keeps two additional 32-bit tensors per parameter). Also account for activations: assume activations across all layers for the batch require ~1.5x the parameter memory. Show the math and then list practical techniques to reduce peak memory usage so the model fits on a 16GB GPU.

HardTechnical

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An edge device must run inference with a 50ms latency budget per frame and has a 3W sustained power limit. The current model requires 200 MFLOPs per inference and the device delivers 10ms per 100 MFLOPs at 2W. Propose concrete model compression and runtime strategies (pruning, quantization, architecture search, DVFS, batching) to meet the power-latency budget. Quantify expected improvements and tradeoffs to accuracy and power.

EasyTechnical

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Explain Big O, Big Theta, and Big Omega notation. For each notation: give the formal definition, provide one concrete algorithmic example where the three notations differ (for example: linear search, binary search, quicksort), and explain the difference between average-case and worst-case complexity. As a Machine Learning Engineer, briefly explain why distinguishing average vs worst-case matters for both training and inference systems in production.

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