Algorithmic Use of the Mal’cev Correspondence

Applications of Lie Methods to Computations with Polycyclic Groups

In this thesis we demonstrate the algorithmic usefulness of the so-called Mal’cev correspondence for computations with infinite polycyclic groups. This correspondence between Q-powered nilpotent groups and rational nilpotent Lie algebras was discovered by Anatoly Mal’cev in 1951. We show how the Mal’cev correspondence can be realized on a computer. We explore two possibilities for this purpose ...

Using the Mal’cev correspondence for collection in polycyclic groups

We describe several approaches for realizing the Mal’cev correspondence between Q-powered nilpotent groups and nilpotent Lie algebras over Q. We apply it to fast collection in polycyclic groups. Our methods are fully implemented and publicly available. We report on the implementation and give runtimes for some example groups.

The Mal’cev correspondence for counting problems in groups and rings

Parallel Genetic Algorithm Using Algorithmic Skeleton

Algorithmic skeleton has received attention as an efficient method of parallel programming in recent years. Using the method, the programmer can implement parallel programs easily. In this study, a set of efficient algorithmic skeletons is introduced for use in implementing parallel genetic algorithm (PGA).A performance modelis derived for each skeleton that makes the comparison of skeletons po...

The Role of Algorithmic Applications in the Development of Architectural Forms (Case Study:Nine High-Rise Buildings)

The process of developing architectural forms has greatly been changed by advances in digital technology, especially in design tools and applications. In recent years, the advent of graphical scripting languages in the design process has profoundly affected 3D modeling. Scripting languages help develop algorithms and geometrical grammar of shapes based on their constituent parameters. This stud...