I am a geometric group theorist. Geometric group theory is a highly interdisciplinary field focusing on the study of groups via their actions on geometric spaces. Geometric group theory uses the tools and approaches of algebraic topology, commutative algebra, semigroup theory, hyperbolic geometry, geometric analysis, combinatorics, computational group theory, computational complexity theory, lo...

We consider communication structures for event ordering algorithms in distributed environments where information ows only in one direction. Example applications are multilevel security and hierarchical databases. Although the most general one-directional communication structure is a partial order, partial orders do not enjoy the property of being consistently-ordered, a formalisation of the not...

Akl, S., G. Laborite, M. Leeder and K. Qiu, On doing Todd-Coxeter coset enumeration in parallel, Discrete Applied Mathematics 34 (1991) 27-35. The Todd-Coxeter coset enumeration method is without any doubt the best known and most used method in computational group theory. Surprisingly, however, it seems that no attempt has yet been made at producing a parallel version of it. This paper reports ...

Prior to this paper all small simple groups were known to be efficient but the status of four of their covering groups was unknown. We produce nice efficient presentations for all of these groups, resolving the previously unknown cases. We give presentations that are better than available before in terms of length and in terms of computational properties. In many cases our presentations have mi...

The Todd-Coxeter coset enumeration algorithm is one of the most powerful tools of computational group theory. It may be viewed as a means of constructing permutation representations of nitely presented groups. In this paper we present an analogous algorithm for directly constructing matrix representations over many elds. In fact the algorithm is more general than this, and can be used to constr...

In this paper, we propose a novel approach to perform efficient motion estimation specific to surveillance videos. A real-time background subtractor is used to detect the presence of any motion activity in the sequence. Two approaches for selective motion estimation, GOP-by-GOP and Frame-byFrame, are implemented. In the former, motion estimation is performed for the whole group of pictures (GOP...

Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational group theory may be used to gain insight into the general structure of algebraic algorithms. This paper examines the basic ideas behind some of the more impor...

This paper presents a novel method to simplify stochastic workflow networks for their performance analysis under a unified computable framework. This method is based on two techniques: (1) module simplification, and (2) PH equivalence and PH approximation. In the first technique, simplified procedures for at least four crucial modules: sequential routing, parallel routing, selective routing and...

We present a new structural framework for computational group theory, based on chains of subgroups. This extends existing methods, such as Schreier-Sims techniques for permutation groups. This framework is now a part of the GAP 4 computational algebra system. It will be useful for implementing the matrix group recognition project.