Computational Complexity

Abstract

Solving a mathematical problem will require calculations. Whether such calculations are performed manually or on a computer, we will be interested in the effort it will take to perform these calculations. Since the days of the abacus, the slide rule, and the mechanical calculating machine, our ability to handle vast amounts of calculations has developed to an extraordinary extent. However, at the same time, the need for ever more complex and large-scale computations has soared, at times outperforming the increase of computational capability. It is therefore interesting to study the science of how much calculation effort our numerical problems require. This is the topic of this chapter. The treatment in this chapter is based on material from Eiselt and Sandblom (2000). For an original and comprehensive treatment of computational complexity, readers are referred to the classical book by Garey and Johnson (1979).