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Combinatorial Optimization consists of finding an optimal-object from a finite object’s set where exhaustive search may not be feasible. Through this [course_title] you will be able to develop the best airline-network of spokes and destinations, decide which taxis in a fleet to route to pick up fares. This [course_title] will help you understand the topics like non-bipartite-matchings and cover many results extending the fundamental results of matchings, flows, and matroids.

### Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

### Certification

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Course Credit: MIT

### Course Curriculum

 Module: 01 Non-Bipartite Matching: Tutte-Berge Formula, Gallai-Edmonds Decomposition, Blossoms 00:15:00 Non-Bipartite Matching: Edmonds’ Cardinality Algorithm and Proofs of Tutte-Berge Formulas and Gallai-Edmonds Decomposition 00:30:00 Cubic Graphs and Matchings, Factor-Critical Graphs, Ear Decompositions 00:30:00 The Matching Polytope, Total Dual Integrality, and Hilbert Bases 00:30:00 Total Dual Integrality, Totally Unimodularity 00:30:00 Posets and Dilworth Theorem 00:30:00 Partitioning Digraphs by Paths and Covering them by Cycles 00:30:00 Module: 02 Proof of the Bessy-Thomasse Result 00:30:00 Matroids: Defs, Dual, Minor, Representability 00:30:00 Matroids: Representability, Greedy Algorithm, Matroid Polytope 00:30:00 Matroid Intersection 00:30:00 Matroid Intersection, Matroid Union, Shannon Switching Game 00:30:00 Matroid Intersection Polytope, Matroid Union 00:30:00 Matroid Union, Packing and Covering with Spanning Trees, Strong Basis Exchange Properties 00:30:00 Module: 03 Matroid Matching: Examples, Complexity, Lovasz’s Minmax Relation for Linear Matroids 00:30:00 Jump Systems: Definitions, Examples, Operations, Optimization, and Membership 00:30:00 Graph Orientations, Directed Cuts (Lucchesi-Younger Theorem), Submodular Flows 00:30:00 Submodular Flows: Examples, Edmonds-Giles Theorem, Reduction to Matroid Intersection in Special Cases 00:30:00 Splitting Off 00:30:00 Proof of Splitting-Off 00:30:00 Multiflow and Disjoint Path Problems 00:30:00 The Okamura-Seymour Theorem 00:30:00 Assessment Submit Your Assignment 00:00:00 Certification 00:00:00

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