Optimize machines for distributed merging cost

Q: Optimize machines for distributed merging cost

This question evaluates a candidate's ability to perform asymptotic performance analysis and reason about scalability trade-offs between parallel computation and aggregate merge costs.

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Question

Optimize k to Minimize Distributed Runtime

Context

You are splitting a dataset of size n across k identical machines.

Per-machine compute (with even partitioning): O(n/k)
Merge cost of the k partial results: O(k^2)
Other overheads are negligible

Total runtime: T(k) = O(n/k + k^2)

Question

Which value of k approximately minimizes the total runtime? Pick ONE option:

A) around 10
B) around log₂ n
C) around square root of n
D) around n/2

Optimize machines for distributed merging cost

Optimize k to Minimize Distributed Runtime

Context

Question

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Optimize machines for distributed merging cost

Overview

Optimize k to Minimize Distributed Runtime

Context

Question

Solution

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