4. Size Parameters

The execution times of these implementations are displayed with respect to polyhedral size criteria, so that we can observe the relation between the performances and specific sets of polyhedra. In fact, the chosen criteria for filters and statistical characteristics of the databases are numbers related to dimensions, number of constraints (equations and inequalities) and coefficients:

• number of dimensions, i.e. number of variables;
• number of constraints, i.e. number of equations and inequalities;
• the largest coefficient, i.e. magnitude;
• density or sparsity, which is the polyhedron's representative matrix's density (see [YAN93]) .

The above size parameters of constraint systems are determining factors for every polyhedral operation. For practical reasons we have chosen the numbers of dimensions, of constraints and density information. Other factors are expensive to compute, e.g. matrix's determination, and heuristics, which could take advantage of this information to select the most appropriate algorithm, should not require CPU intensive decision procedures.