Optimization problems -- The simplex algorithm -- Duality -- Computational considerations for the simplex algorithm -- The primal-dual algorithm -- Primal-dual algorithms for max-flow and shortest path: ford-fulkerson and dijkstra -- Primal-dual algorithms for min-cost flow -- Algorithms and complexity -- Efficient algorithms for the max-flow problem -- Algorithms for matching -- Weighted matching -- Spanning tree and matroids -- Integer linear programming -- A cutting-planning algorithm for integer linear programs -- NP-complete problems -- More about NP-completeness -- Approximation algorithms -- Branch-and-bound and dynamic programming -- Local search

1. Mathematical optimization
2. Combinatorial analysis
3. Computational complexity