I almost exclusively work on problems can be solved(by a combinatorial algorithm) in polynomial time. I have never used theory of mixed integer linear programs,

I almost exclusively work on problems can be solved(by a combinatorial algorithm) in polynomial time. I have never used theory of mixed integer linear programs, but that's because I focus on different aspects of combinatorial optimization. If I teach an undergrad course, I would model after Michel Goemans's course. http://www-math.mit.edu/~goemans/18433S15/18433.html http://www-math.mit.edu/~goemans/18433S15/18433.html I will also introduce some submodular functions(and touches submodular flow). It captures half of the things encountered in the course, and general and simple enough to be the first thing to try. For example, the following problem might be difficult if one tries to create an algorithm by modify the standard matching algorithms. However, one can easily show it is polynomial time solvable by proving some submodular property. http://cstheory.stackexchange.com/questions/20245/subset-of-a-bipartite-graph-with-maximal-number-of-minimal-unmatched-vertices/33603 http://cstheory.stackexchange.com/questions/20245/subset-of-...