Computing and Complexity — Networks, Nature and Virtual Worlds

Abstract

Modern computing is intimately bound up with complexity theory. This chapter explores this intimate relationship and its applications in complexity theory. The need to deal with complex problems has motivated many ideas and issues in computing. Conversely, computing, and computational ideas, have also played a prominent role in the development of complexity theory. In applications of information technology, complexity arises from the need to handle enormous volumes of information and to solve ever larger and more intricate problems (e.g. multi-objective optimization). Combinatorial explosions in large datasets create problems of high complexity and pose a major challenge for computer science. Several key ideas from complexity theory have dominated the struggle to cope with the inherent complexity of computing and information. One of the greatest needs in computing and information technology is the vexed question of limited time and space. These two issues underlie many of the ideas and methods adopted in computer science. In information science, the term “complexity” is usually taken to mean “computational complexity.” The idea of carving up a large problem into smaller ones enters computing in the everlasting quest for more time and space. Additionally, modern computing on science had been to make it possible to attack complex questions that previously were intractable. By making simulation modeling practical, computers have helped to advance complexity theory in several ways.