Design and Analysis - Greedy Method

Among all the algorithmic approaches, the simplest and straightforward approach is the Greedy method. In this approach, the decision is taken on the basis of current available information without worrying about the effect of the current decision in future.

Greedy algorithms build a solution part by part, choosing the next part in such a way, that it gives an immediate benefit. This approach never reconsiders the choices taken previously. This approach is mainly used to solve optimization problems. Greedy method is easy to implement and quite efficient in most of the cases. Hence, we can say that Greedy algorithm is an algorithmic paradigm based on heuristic that follows local optimal choice at each step with the hope of finding global optimal solution.

In many problems, it does not produce an optimal solution though it gives an approximate (near optimal) solution in a reasonable time.

Components of Greedy Algorithm

Greedy algorithms have the following five components −

A candidate set − A solution is created from this set.

A selection function − Used to choose the best candidate to be added to the solution.

A feasibipty function − Used to determine whether a candidate can be used to contribute to the solution.

An objective function − Used to assign a value to a solution or a partial solution.

A solution function − Used to indicate whether a complete solution has been reached.

Areas of Apppcation

Greedy approach is used to solve many problems, such as

Finding the shortest path between two vertices using Dijkstra’s algorithm.

Finding the minimal spanning tree in a graph using Prim’s /Kruskal’s algorithm, etc.

Where Greedy Approach Fails

In many problems, Greedy algorithm fails to find an optimal solution, moreover it may produce a worst solution. Problems pke Travelpng Salesman and Knapsack cannot be solved using this approach.

Examples

Most networking algorithms use the greedy approach. Here is a pst of few of them −

Travelpng Salesman Problem

Prim s Minimal Spanning Tree Algorithm

Kruskal s Minimal Spanning Tree Algorithm

Dijkstra s Minimal Spanning Tree Algorithm

Graph - Map Coloring

Knapsack Problem

Job Schedupng Problem

We will discuss these examples elaborately in the further chapters of this tutorial.