Problem Classification

Classifying computational problems is paramount in the realm of algorithm design and optimization. It enables algorithm selection by matching problem types with suitable algorithms, streamlining resource allocation for efficient computing, and guiding algorithm development and analysis. By categorizing problems based on their inherent attributes, we can identify common problem-solving strategies and design algorithms tailored to specific problem categories. This classification also aids in benchmarking and evaluating algorithm performance, allowing researchers and practitioners to assess the effectiveness of various algorithms in solving similar problem types, ultimately advancing the field of algorithmic research and development.

By The Goal

• Find one solution that satisfies the requirements - search

• Find all solutions that satisfy the requirements - enumeration

• Find the best solution according to an objective - optimization

• Determine whether at least one qualifying solution exists (yes/no) - decision

• Count the qualifying solutions - counting

• Find the output of a mathematical or logical function - evaluation problem

These labels describe the requested output, not the algorithm used. A problem may have several related formulations. Enumerating all solutions can be used to find one, decide whether any exist, count them, or select the best one, but an algorithm may solve those goals directly without enumerating every solution. Search asks for a witness; decision asks only whether a witness exists.