CS 787 : Advanced Algorithms Greed

An algorithm that uses the greedy method attempts to construct an optimal (compound) solution to a problem by optimally constructing components one by one. In general, building up locally optimal components may not yield a globally optimal overall solution, but a greedy algorithm will give an optimal result if these two coincide. There are two main issues that arise when applying the greedy approach. First, in developing a greedy algorithm, the order in which we consider components of the problem is crucial. Second, we must also ensure the correctness of our greedy approach, i.e. we must prove that the greedy solution is an optimal one. We will discuss two different methods of proof that achieve these objectives.