Bottom up solution
Aka Divide and conquer. A bottom-up way of constructing the solution.
This includes Dynamic programming, which is discussed in the Optimization survey.
Time Analysis
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Greedy algorithms
Eg: shortest path algorithm.
The matroid
This is a pair: (Set, Independence property). Eg: (vertices, Independent sets in a graph). There are efficient algorithms for finding the maximal indpendent subset. So, often sufficient to specify the problem using the matroid formalism.