ALGORITHM ARTICLE
Connected components
Problem. Partition an undirected graph into maximal reachable sets.
Core idea. One traversal from an unseen seed discovers exactly one component.
Procedure
- Choose an unseen vertex.
- Traverse every reachable neighbor.
- Record the component and repeat.
Certificate. Every vertex appears once and each set is reachability-closed.
Data structures and API
from optfin_orlab import ExactGraphOracle
solver = ExactGraphOracle()
result = solver.connected_components(...)Complexity. O(|V|+|E|)
Limits. Not a strongly-connected-components routine for directed graphs.
OPTFIN AUDIT CHECKS
What has to reconcile before this method is trusted.
- DefinitionProblem, objective, inputs and output are explicit.
- Data structureThe public API and canonical source path are identified.
- CorrectnessEvery vertex appears once and each set is reachability-closed.
- ComplexityO(|V|+|E|)
- Operational limitNot a strongly-connected-components routine for directed graphs.
- ReproductionSource, executable test and evidence route remain linked.
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