AI workflows are fundamentally dependency problems best modeled as Directed Acyclic Graphs (DAGs). Topological sort converts a DAG into a valid execution order, ensuring producers always run before consumers. Beyond ordering, this approach enables parallelism by identifying independent tasks that can run concurrently, detects circular dependencies before execution begins (preventing deadlocks), and supports incremental re-execution by traversing only affected subgraphs when a task fails. Multi-agent frameworks like LangGraph use the same DAG model to orchestrate agents without hardcoded sequencing logic. Key pitfalls include fan-in bottlenecks where a merge node waits on the slowest parallel task, and the importance of catching cycle errors at definition time rather than runtime.
