Point sets and frame algorithms in management

• Authors: José H. Dulá
• Venue: AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
• Year: 2005

Consider a finite point set $\mathcal{A}$ in m-dimensional space and the polyhedral hulls it generates from constrained linear combinations of its elements. There are several interesting management problems that are modelled using these point sets and the resulting polyhedral objects. Examples include efficiency/performance evaluation, ranking and ordering schemes, stochastic scenario generation, mining for the detection of fraud, etc. These applications require the identification of frames; that is, the extreme elements of the polyhedral sets, a computationally intensive task. Traditional approaches require the solution of an LP for each point in the point set. We discuss this approach as well as a new generation of faster, output-sensitive, algorithms.