Before we dive deep into this section, let's first define two terms:

• Algorithmic overheads: Whenever we try to find the optimal solution to a certain problem, it takes some time. As the problems that we are trying to optimize become more and more complex, the time it takes to find the optimal solution also increases. We represent algorithmic overheads with Ω_i.
• Delta from optimal: For a given optimization problem, there exists an optimal solution. Typically, we iteratively optimize the solution using our chosen algorithm. For a given problem, there always exists a perfect solution, called the optimal solution, to the current problem. As discussed, based on the classification of the problem we are trying to solve, it's possible for the optimal solution to be unknown or that it would take an unreasonable amount of time to calculate and verify it. Assuming that the optimal solution is known, the difference from optimal for the current solution in the i^th iteration is called delta from optimal and is represented by Δ_i.

For complex problems, we have two possible strategies:

• Strategy 1: Spend more time finding a solution nearest to optimal so that Δ_i is as small as possible.
• Strategy 2: Minimize the algorithmic overhead, Ω_i . Use the quick-and-dirty approach and just use a workable solution.

Greedy algorithms are based on strategy 2, where we do not make an effort to find a global optimal and choose to minimize the algorithm overheads instead.

Using a greedy algorithm is a quick and simple strategy of finding the global optimal value for multistage problems. It is based on selecting the local optimal values without making an effort to verify whether local optimal values are globally optimal as well. Generally, unless we are lucky, a greedy algorithm will not result in a value that can be considered globally optimal. However, finding a global optimal value is a time-consuming task. Hence, the greedy algorithm is fast compared to the divide-and-conquer and dynamic programming algorithms.

Generally, a greedy algorithm is defined as follows:

1. Let's assume that we have a dataset, D. In this dataset, choose an element, k.
2. Let's assume the candidate solution or certificate is S. Consider including k in the solution, S. If it can be included, then the solution is Union(S, e).
3. Repeat the process until S is filled up or D is exhausted.