7 skills · sorted by relevance
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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Algorithms for decomposing DAGs into chains for parallel execution and resource optimization
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Graph algorithms for detecting and resolving cycles in directed graphs and workflow definitions
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Expert-level graph theory knowledge. Use when working with graph algorithms, network flows, matching, graph coloring, planar graphs, spectral graph theory, random graphs, or graph applications in computer science and networks. Also use when the user mentions 'shortest path', 'minimum spanning tree', 'network flow', 'bipartite matching', 'graph coloring', 'clique', 'independent set', 'vertex cover', 'planarity', 'graph isomorphism', 'adjacency matrix', or 'Laplacian'.
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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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Validate finite-DAG order objectives and construct reachability-chain or direct-edge path partitions with explicit proof boundaries. NOT for equating reachability chains with direct-edge paths without checking the chosen objective.
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Analyze undirected cycle structure within a valid DAG using the source paper's orientation and contraction method. Use for cycle-basis analysis with explicit graph and reduction choices. NOT for directed feedback loops, workflow deadlocks, or runtime resilience claims.
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