# Problem Abstraction/Reduction

## Problem Abstraction/Reduction

Problem Abstraction

• Problem abstraction refers to the process of isolating the underlying essence of a problem, stripping away specific details and context to reveal the general principles that underlie the problem.

• This concept is fundamental in computer science, especially in algorithm design and computational problem solving, as it allows problems to be solved in a more general manner.

• Problem abstraction uses a top-down design approach – breaking down a problem into smaller, manageable parts.

Characteristics of Problem Abstraction

• Generality: By metaphorically ‘zooming out’ to target the essential nature of a problem, problem abstraction allows a solution to be applied broadly, thus making it more reusable.

• Simplicity: Problem abstraction aims to transform complex problems into simpler, more general problems, making them easier to understand and resolve.

Problem Reduction

• Problem reduction, also known as problem transformation, is a strategy whereby a difficult problem is transformed or ‘reduced’ into a different problem that is easier to solve.

• The solution to the transformed problem is then used to find a solution to the original problem.

• Examples of problem transformation include transforming a problem into a sorted variant of the problem, or transforming a continuous problem into a discrete problem.

Problem Reduction Strategies and Methods

• Recursion: Some problems can be reduced to simpler instances of the same problem. This recursive approach is often used in search and sorting algorithms.

• Iteration: Other problems can be transformed into an iterative process with incremental steps that bring it closer to a solution with each cycle.

• Simplification: A problem can sometimes be simplified by removing some of its constraints temporarily, solving the simpler problem and then reintroducing the constraints back in an orderly fashion.

Benefits of Problem Abstraction and Reduction

• Universal problem solving: These approaches allow for greater adaptability. Once a solution is found, it can be applied to many similar types of problems, not just to the specific instance that was initially considered.

• Efficiency: Problem reduction typically transforms problems into easier versions that can be solved more efficiently.

• Understanding and comprehension: Breaking down complex problems into more manageable parts by means of abstraction and reduction can make them much easier to understand and approach.

Mastering the concepts of problem abstraction and reduction are important in computer science because they provide a structured framework for approaching complex problems and designing efficient algorithms. By using these strategies, challenging computational tasks become much easier to solve.

These concepts are also fundamental to grasping the notion of computational complexity and appreciating how some problems may be inherently difficult to solve – a further area explored in the study of theoretical computer science.