We found that sampling and the chosen filter criterion were reasonable for the total execution times of all the necessary operations. Moreover, during our early experiments, we have tested some other databases with different intervals and criteria to compare their results, and found out that our choice were good enough to obtain reliable results, with only one exception described in 6_sec:convex_hull_results. For instance, we have basically the same conclusions with and sampling for satisfiability test. The sampling and full projection databases also give similar results.
Note here that even with the sampling rate, we still have a very large number of constraint systems that relatively assures accurate measurement. 6_tab:projection_databases, 6_tab:minimization_databases and 6_tab:convex_hull_databases present the two types of databases for the projection, minimization and convex hull operators. We remark that their sampled databases are smaller than satisfiability test's, and their filtered databases are useless.