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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
3
votes
Interesting and accessible topics in graph theory
This is probably not what you're looking for, but if I were teaching such a course I'd focus on the interplay between algorithms for various graph problems and the more traditional mathematical approa …
2
votes
Greedy approach to 0-1 Knapsack problem in specific instances
As Frederico has already shown, this isn't enough to make the greedy heuristic immune to counterexamples.
It's worth mentioning that there is a simple dynamic programming algorithm for the knapsack …