4. Polyhedral size statistics:

For the filtered databases, we have seen different results between PerfectClub and SPEC95 tests: the $C^3$ Double Description method has many timeout exceptions with PerfectClub tests but it has only $22$ overflows and no timeout exception, much better performance compared to the other three algorithms.

Table 10: Average polyhedral size statistic of filtered database

Filtered databases	PerfectClub	SPEC95
ASCII file size	5596.73	2496.27
Average #Dimensions	46.97	10.28
Average #Equations	17.40	2.35
Average #Inequalities	38.89	52.56
Average #Constraints	56.30	54.91
Average #Sparsity index	3.90	3.86
Average #Vertices	1118.76	18.66
Average #Rays	69.10	14.07
Average #Lines	6.78	0.53

6_tab:satisfiability_poly_size_stat_filter compares the two databases, where the differences in space dimensions, numbers of vertices, rays and lines are important since the Double Description method is related to these factors. Therefore, the cause of the difference is the polyhedral characteristics of the filtered databases.