A Comprehensive Review of Classical Algorithm Design Techniques

Abstract

Algorithm design is a well-established research area, actively pursued since the mid-1950s. Classical algorithm design techniques for solving combinatorial and optimization problems typically yield polynomial-time solutions. These techniques and their real-world applicability remain relevant despite significant advances in computer science and their constraints. Still actively taught, they warrant comprehensive review.

A thorough survey of basic algorithm design methods, touches on fundamental techniques for solving a wide range of problems. Fundamental steps in problem formulation clarify domain knowledge prior to algorithm selection. Four well-known techniques for solving mathematical problems are addressed: divide and conquer, dynamic programming, greedy algorithms, and graph algorithms. Emphasis is placed on brief but mathematically precise treatments rather than exhaustive bibliographies, and all detailed case studies address familiar examples readily encountered in academic literature or teaching materials.

Keywords: Algorithm design, combinatorial and optimization problems, techniques.