Algorithm

Computer algebra systems such as Maple compute using mathematical formulae as well as numbers, mechanizing the mathematics used in education and research labs. This project focuses on the design and implementation of algorithms for these systems. Emphasis is placed on efficiency that allows large and complex problems of the type encountered in industrial settings to be solved. In the past year the team has made major advances in the core tools that are needed to solve these complex problems.

Algorithms for solving difficult computational problems play a key role in many applications, including scheduling, resource allocation, computer-aided design, and software verification. In many cases, heuristic methods are the key to solving these problems effectively. However, the design of effective heuristic algorithms, particularly algorithms for solving computationally hard problems, is a difficult task that requires considerable expertise.

Efficiency in modern industrial operations requires that available resources are deployed in an optimal manner. The study of facility location is concerned with the placement of one of more facilities in a way that meets a particular objective, such as minimizing transportation costs, providing a high level of service to customer or capturing market share. This project, by exploiting the mathematics of computational geometry and algorithmic graph theory, develops new tools to aid in the location of facilities to optimally serve the demands of customers.

Statistical machine learning is an endeavor in which statisticians and computer scientists use computation to identify useful information from large amounts of data. Telecommunications, insurance and pharmaceutical companies use the team’s machine learning and data mining techniques to determine customer patterns, predict future customer behavior and better understand their needs. The project addresses some of the main practical and theoretical difficulties encountered when dealing with large datasets.