Topics in Combinatorial Optimization

Calendar

LEC #	TOPICS
1	Non-Bipartite Matching: Tutte-Berge Formula, Gallai-Edmonds Decomposition, Blossoms
2	Non-Bipartite Matching: Edmonds’ Cardinality Algorithm and Proofs of Tutte-Berge Formulas and Gallai-Edmonds Decomposition
3	Cubic Graphs and Matchings, Factor-Critical Graphs, Ear Decompositions
4	The Matching Polytope, Total Dual Integrality, and Hilbert Bases
5	Total Dual Integrality, Totally Unimodularity Matching Polytope and the Cunningham-Marsh Formula Showing TDI
6	Posets and Dilworth Theorem Deduce Konig’s Theorem for Bipartite Matchings Weighted Posets and the Chain and Antichain Polytopes
7	Partitioning Digraphs by Paths and Covering them by Cycles Gallai-Milgram and Bessy-Thomasse Theorems Cyclic Orderings
8	Proof of the Bessy-Thomasse Result The Cyclic Stable Set Polytope
9	Matroids: Defs, Dual, Minor, Representability
10	Matroids: Representability, Greedy Algorithm, Matroid Polytope
11	Matroid Intersection
12	Matroid Intersection, Matroid Union, Shannon Switching Game
13	Matroid Intersection Polytope, Matroid Union
14	Matroid Union, Packing and Covering with Spanning Trees, Strong Basis Exchange Properties
15	Matroid Matching: Examples, Complexity, Lovasz’s Minmax Relation for Linear Matroids
16	Jump Systems: Definitions, Examples, Operations, Optimization, and Membership
17	Jump Systems: Membership (cont.)
18	Graph Orientations, Directed Cuts (Lucchesi-Younger Theorem), Submodular Flows
19	Submodular Flows: Examples, Edmonds-Giles Theorem, Reduction to Matroid Intersection in Special Cases
20	Splitting Off $k$-Connectivity Orientations and Augmentations
21	Proof of Splitting-Off Submodular Function Minimization
22	Multiflow and Disjoint Path Problems Two-Commodity Flows
23	The Okamura-Seymour Theorem and the Wagner-Weihe Linear-Time Algorithm