Combinatorial Optimization
Explore discrete structures; network algorithms; complexity and approximations. Concepts and connections are available independently of video coverage.
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Matroids
A matroid abstracts independence through hereditary and exchange axioms.
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Graph matchings
A matching is a set of edges with no shared endpoints.
Shortest path models
Dijkstra solves non-negative networks; Bellman-Ford tolerates negative edges and underpins route pricing.
Approximation algorithms
An approximation algorithm provides a provable ratio to the optimum under stated assumptions.
Assignment problem
A costed one-to-one pairing can be optimized using matching or linear programming structure.
Bipartite matching
Matching in a two-part graph pairs vertices across parts without shared endpoints.
Knowledge connections
- Graph matchings · Related · Map context
- Shortest path models · Related · Map context