Introduction to Greedy Algorithms

What is Greedy Algorithm?

Greedy is an algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit. So the problems where choosing locally optimal also leads to global solution are the best fit for Greedy.

Characteristics of Greedy algorithm:

For a problem to be solved using the Greedy approach, it must follow a few major characteristics:

• There is an ordered list of resources(profit, cost, value, etc.) 
• Maximum of all the resources(max profit, max value, etc.) are taken. 
• For example, in the fractional knapsack problem, the maximum value/weight is taken first according to available capacity. 

Examples of Greedy Algorithm :

Some Famous problems that exhibit Optimal substructure property and can be solved using Greedy approach are :

1. Job sequencing Problem
2. Fractional Knapsack Problem
3. Prim’s algorithm to find Minimum Spanning Tree
4. Activity Selection Problem
5. Dijkstra’s shortest path algorithm

Advantages of the Greedy Approach: 

• The greedy approach is easy to implement and typically have less time complexity.
• Greedy algorithms can produce efficient solutions in many cases, especially when the problem has a substructure that exhibits the greedy choice property.
• Greedy algorithms are often faster than other optimization algorithms, such as dynamic programming or branch and bound, because they require less computation and memory.
• The greedy approach can be applied to a wide range of problems, including problems in computer science, operations research, economics, and other fields.
• The greedy approach can be used to solve problems in real-time, such as scheduling problems or resource allocation problems, because it does not require the solution to be computed in advance.
• Greedy algorithms can be used in conjunction with other optimization algorithms, such as local search or simulated annealing, to improve the quality of the solution.

Disadvantages of the Greedy Approach:

• The local optimal solution may not always be globally optimal.
• Greedy algorithms do not always guarantee to find the optimal solution, and may produce suboptimal solutions in some cases.
• The greedy approach relies heavily on the problem structure and the choice of criteria used to make the local optimal choice. If the criteria are not chosen carefully, the solution produced may be far from optimal.
• Greedy algorithms may require a lot of pre-processing to transform the problem into a form that can be solved by the greedy approach.
• Greedy algorithms may not be applicable to problems where the optimal solution depends on the order in which the inputs are processed.

Some of the Important Greedy Algorithms are given below:

In the dynamic landscape of algorithmic design, Greedy Algorithms stand out as powerful tools for solving optimization problems. Aspirants preparing for the GATE Exam 2024 are poised to encounter a range of questions that test their understanding of Greedy Algorithms. These notes aim to provide a concise and insightful overview, unraveling the principles and applications of Greedy Algorithms that are likely to be scrutinized in the upcoming GATE examination.