Schedule dependent services with layered startup

Q: Schedule dependent services with layered startup

This question evaluates understanding of graph algorithms (topological ordering and cycle detection), layered dependency extraction, and parallel scheduling under resource constraints, testing algorithm design and complexity reasoning in the Coding & Algorithms domain.

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Question

You are given N services and dependency pairs (u -> v) meaning u must start before v.

Produce a valid startup order if one exists; otherwise detect and report a cycle.
Output the services by dependency layers (all in-degree-0 services first, then the next layer, etc.).
Given each service i has a startup time t[i] and there are K CPU cores, schedule startups to minimize total completion time while respecting dependencies; describe your algorithm, complexity, and practical heuristics for parallel execution.

Schedule dependent services with layered startup

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