Combinatorial Optimization
Explore discrete structures; network algorithms; complexity and approximations. Concepts and connections are available independently of video coverage.
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Approximation algorithms
An approximation algorithm provides a provable ratio to the optimum under stated assumptions.
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Integer relaxations
Removing integrality yields easier problems whose optima can bound the discrete optimum.
NP-completeness
An NP-complete decision problem lies in NP and admits polynomial reductions from every NP problem.
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.
Graph matchings
A matching is a set of edges with no shared endpoints.
Knowledge connections
- NP-completeness · Related · Map context
- Integer relaxations · Related · Map context