Abstract
The study of algorithm complexity and the use of asymptotic notation is an important area in the field of computer science. Complexity deals with algorithm efficiency, that is, how efficient the potential problem solutions are in terms of their execution time. Algorithms can be represented in pseudocode or in program code. A new model to represent programs is the Geometric Representation of Programs (GRP) model developed by d'Auriol (1999). The GRP model is used to represent programs in a geometric framework, the programs are represented, in part, by geometric objects.

There is no existing method at present to find the complexity of algorithms in the GRP model. This thesis proposes a model called the Volume Complexity Model to find the complexity of programs represented in GRP. The volume of a geometric object can be thought of as representing characteristics associated with complexity. Thus, it is meaningful to calculate the volume of a geometric object. Hence, this thesis deals with the issue of how best volumes can be correlated to the problem of finding the complexity of programs in GRP. The main objective of this work is to enhance the existing GRP model in a new and logical direction so as to make the model more application oriented.