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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.