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Microsoft·Software Engineer·Onsite - Coding / Algorithms·Senior

Senior
Apr 2026

Summary

Microsoft SWE interview with a graph partitioning problem that's basically NP-hard territory. They wanted you to reason through heuristics and then actually implement something, which is a lot to ask in one sitting.

Questions Asked (1)

Q1

You have a graph where nodes are GPUs and edges represent links between them. Partition all nodes into exactly X balanced groups (each group has either floor(N/X) or ceil(N/X) members) such that the number of edges whose both endpoints are in the same group is maximized. Walk through possible approaches and implement one.

Algorithms & Data StructuresTechnical Trade-offsSystem Design
Author's notes

This is a follow-up to an earlier GPU grouping question, so if you haven't seen the first part you're already behind.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem: this is a balanced graph partitioning problem, which is NP-hard. Discuss the trade-offs between exact and heuristic methods, then implement a practical heuristic like greedy or local search, explaining its complexity and why it's suitable for the given constraints.

Pro tip: Acknowledge the NP-hardness upfront and propose a heuristic that balances solution quality and runtime, showing you understand real-world constraints. Mention that for small graphs, exact methods like branch-and-bound could be used, but for large-scale GPU clusters, heuristics are necessary.

1. Clarify problem and constraints

Confirm the graph size, density, and whether the partition must be exactly balanced. Discuss the NP-hard nature of balanced graph partitioning.

2. Explore approaches

Outline exact methods (e.g., integer programming, branch-and-bound) and heuristics (greedy, Kernighan-Lin, spectral, local search). Compare their trade-offs in terms of optimality, complexity, and scalability.

3. Choose and justify an approach

Select a heuristic suitable for the problem scale, such as a greedy algorithm with local refinement. Explain why it's a good fit given typical constraints.

4. Implement the algorithm

Write clean, efficient code for the chosen heuristic. Include comments on key steps and handle edge cases like disconnected graphs or uneven group sizes.

5. Analyze and test

Discuss time and space complexity, and suggest test cases (small graphs, random graphs, worst-case). Mention potential improvements like multi-start or simulated annealing.

Key Points to Mention

  • NP-hardness of balanced graph partitioning and its implications
  • Trade-offs between exact and heuristic algorithms
  • Greedy algorithm: assign nodes to groups to maximize internal edges while maintaining balance
  • Local search refinement: swap nodes between groups to improve objective
  • Time complexity: O(E + N log N) for greedy, O(N^2) per iteration for local search
  • Scalability considerations for large GPU clusters and potential parallelization

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.