Chapter 4. Analysis of Algorithms

Introduction and Motivation

Analyzing the properties of algorithms is fundamental for drawing conclusions on their applicability, for the comparison of different algorithms, and for the development of new ideas that help to improve existing algorithms. An algorithm that solves a problem optimally while the time and space it consumes grow not too fast is the ideal case. Unfortunately, such algorithms are not known to exist for many optimization problems that occur frequently in industrial applications. For these problems one can look for trade-offs between different properties like, e. g., the quality of the solution and the running time of the algorithm. Another possibility for coping with these problems is to relax the requirement that an algorithm has to work well on all instances of the considered optimization problem. It is sufficient if the algorithm performs well on those instances that occur typically in the considered application.