Model the test cases as a directed acyclic graph (DAG) with dependencies as edges and hardware constraints as node attributes. Use topological sort to detect cycles and produce a valid order, then apply list scheduling with heuristics like critical path or longest processing time to assign tasks to heterogeneous GPU executors, minimizing makespan. Discuss complexity and trade-offs between optimality and scalability.
Pro tip: Emphasize that in real-world systems, perfect load balancing is NP-hard, so practical solutions use heuristics and may incorporate dynamic feedback from executors to adapt to runtime variability.
Represent test cases as nodes, dependencies as directed edges, and hardware/driver constraints as node labels or edge conditions. This forms a directed graph that may contain cycles if dependencies are invalid.
Use DFS or Kahn's algorithm to detect cycles. If acyclic, compute a topological ordering that respects dependencies. Discuss time O(V+E) and space O(V+E).
Model executors as machines with different speeds and capabilities. Use list scheduling: assign tasks in topological order to the executor that minimizes completion time, considering constraints. Discuss heuristics like critical path, longest processing time, and bin packing.
Topological sort is O(V+E). Scheduling is NP-hard in general; heuristics run in O(V log V + E) or O(V^2). Discuss approximation ratios and scalability for tens of thousands of nodes.
Mention static vs dynamic scheduling, work stealing, and feedback loops to handle runtime variability. Discuss how to minimize wall-clock time by balancing load and minimizing idle time.
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