ALGORITHM ARTICLE
Kruskal minimum spanning tree
Problem. Minimum-cost connection of every vertex in a weighted undirected graph.
Core idea. Accept the lightest edge that joins different components.
Procedure
- Sort edges by weight.
- Reject cycle-forming edges with disjoint sets.
- Stop after |V|-1 accepted edges.
Certificate. A spanning acyclic edge set; optimality follows from the cut property.
Data structures and API
from optfin_orlab import ExactGraphOracle
solver = ExactGraphOracle()
result = solver.minimum_spanning_tree(...)Complexity. O(|E| log |E|)
Limits. A disconnected graph produces a forest.
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.
- CorrectnessA spanning acyclic edge set; optimality follows from the cut property.
- ComplexityO(|E| log |E|)
- Operational limitA disconnected graph produces a forest.
- ReproductionSource, executable test and evidence route remain linked.
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