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4. Chosen Criteria:

We found that $1\%$ 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 $10\%$ and $1\%$ sampling for satisfiability test. The $1\%$ sampling and full projection databases also give similar results.


Table 1: Satisfiability Test: Numbers of constraint systems
  PerfectClub SPEC95
Sampled Database ($1\%$) 12668 16303
Filtered Database 1310 4676


Note here that even with the $1\%$ 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.


Table 2: Projection: Numbers of constraint systems - filtered databases useless
  PerfectClub SPEC95
Sampled Database ($1\%$) 1789 2583
Filtered Database 3 5



Table 3: Minimization: Numbers of constraint systems - filtered databases useless
  PerfectClub SPEC95
Sampled Database ($1\%$) 3894 4608
Filtered Database 11 12



Table 4: Convex Hull: Numbers of constraint systems - empty filtered databases
  PerfectClub SPEC95
Sampled Database ($1\%$) 194 pairs 240 pairs
Filtered Database 0 0



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Previous: 3. Incoherent Databases: Up: 8. Polyhedral Databases Next: 9. Distribution of Dimension
Nguyen Que Duong
2006-09-16