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Apply practical DAG decomposition, transitive-edge reduction, and reachability indexing to dense dependency graphs. Use when low width and repeated queries justify preprocessing. NOT for cyclic graphs, one-off graph checks, or exact-minimum-chain requirements.
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Decompose DAGs into execution chains using width bounds, stratification, virtual nodes, and matching. Use when minimizing workflow lanes in dependency graphs. NOT for cyclic graphs, generic scheduling, or one-off queries with no preprocessing payoff.
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Analyze hierarchical DAG-like systems by separating undirected substrate from ordering metadata, then classifying diamonds, mixers, shortcuts, and hidden cycle structure. Use for workflow architecture, citation or genealogy DAG comparison, and information-flow diagnosis. NOT for ordinary cycle detection in arbitrary graphs, one-node runtime debugging, or systems with no real ordering constraint.
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Parses complex problems into candidate DAG (Directed Acyclic Graph) execution structures. Decomposes tasks into nodes with dependencies and identifies candidate parallelization opportunities. Activate on 'build dag', 'create workflow graph', 'decompose task', 'execution graph', 'task graph'. NOT for simple linear tasks or when an existing DAG structure is provided.
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Define time-varying amplitudes. Use when user mentions ramp, time-varying, cyclic, pulse, or gradually increasing loads. Does NOT handle static constant loads.
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