Parameterized Polyhedra and Their Vertices

Algorithms specified for parametrically sized problems are more general purpose and more reusable than algorithms for fixed sized problems. For this reason, there is a need for representing and symbolically analyzing linearly parameterized algorithms. An important class of parallel algorithms can be described as systems of parameterized affine recurrence equations (PARE). In this representation, linearly parameterized polyhedra are used to describe the domains of variables. This paper describes an algorithm which computes the set of parameterized vertices of a polyhedron, given its representation as a system of parameterized inequalities. This provides an important tool for the symbolic analysis of the parameterized domains used to define variables and computation domains in PAREs. A library of operations on parameterized polyhedra based on the Polyhedral Library has been written in C and is freely distributed.