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Table 5 Runtime of the Berge algorithm with and without preprocessing (PP) for two intervention problems I ( T , D , n ) with differing n

From: Comparison and improvement of algorithms for computing minimal cut sets

  E2 E1 E0
|D| 489 (0.88%) 489 (0.10%) 489 (0.00%)
|T| 55,177 (99.12%) 484,680 (99.90%) 124,340,727 (100.00%)
   n2=40; n2/|D|=0.08  
MCSs 4 11 44
Min. deletions 5 8 16
Max. deletions 5 8 17
    Without PP   With PP   Without PP   With PP     Without PP     With PP
System size   60×55,177   13×1   64×484,680   17×3     75×124,340,727     28×6
Reading EMs (sec) 0.031 (26%) 0.035 (43%) 0.281 (26%) 0.308 (37%) 71.858 (24%) 76.274 (26%)
Preprocessing (sec) 0.078 (65%) 0.044 (55%) 0.717 (65%) 0.495 (60%) 194.328 (64%) 202.539 (69%)
Calculate MCSs (sec) 0.011 (9%) 0.001 (2%) 0.100 (9%) 0.021 (3%) 35.866 (12%) 15.294 (5%)
Total (sec) 0.121 (100%) 0.081 (100%) 1.099 (100%) 0.823 (100%) 302.053 (100%) 294.108 (100%)
   n2=40; n2/|D|=0.08  
MCSs 72 274 1,720
Min. deletions 5 6 14
Max. deletions 7 10 19
     Without PP    With PP    Without PP    With PP     Without PP     With PP
System size    60×55,177    47×2,295    64×484,680    51×8,664     75×124,340,727     62×321,272
Reading EMs (sec) 0.031 (10%) 0.033 (25%) 0.277 (7%) 0.308 (20%) 71.084 (3%) 77.771 (5%)
Preprocessing (sec) 0.078 (26%) 0.083 (65%) 0.715 (17%) 1.162 (76%) 193.805 (7%) 1,493.367 (94%)
Calculate MCSs (sec) 0.196 (64%) 0.012 (10%) 3.136 (76%) 0.068 (4%) 2,475.110 (90%) 15.909 (1%)
Total (sec) 0.306 (100%) 0.128 (100%) 4.129 (100%) 1.539 (100%) 2,740.004 (100%) 1,587.053 (100%)
  1. In all cases D are identical and T chosen such that it contains all remaining EMs. Note that the columns “without PP” state the runtimes without performing step 1 to 4 of our PP procedures. However, we still sort EMs in ascending order of norm. This is why PP-time is not zero even in the cases without PP. The row “system size” refers to the dimensions of the network, which enters the Berge-algorithm, i.e. after PP.