Advances in Operations Research

Research Article

Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

Table 5

Comparison of selected variants of formulations EC, DCut and SCF on the instances from SET-III with | 𝑉 | = 1 0 0 ; 𝛼 = 1 .
| 𝐿 | = 1 / 4 ⋅ | 𝐸 | | 𝐿 | = 3 / 4 ⋅ | 𝐸 |
𝑑 alg cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts
0.05 EC 10 10 19.6 2 1892 1722 10 0 61.6 7200 108393 124719
E C t 10 10 19.6 23 6887 6026 10 1 51.3 6480 178187 195559
E C t n 10 10 19.6 14 4944 4486 10 2 51.2 5760 163875 182801
E C n 10 10 19.6 2 1491 1246 10 0 62.5 7200 103413 119245
E C s n 10 10 19.6 1 1313 966 10 0 55.5 7200 133833 151889
DCut 10 10 19.6 35 5214 3026 10 0 50.7 7200 367146 337417
D C u t t 10 10 19.6 34 4174 2487 10 4 49.8 4381 76629 55867
D C u t t n 10 10 19.6 12 1148 759 10 6 49.8 3195 87152 60318
D C u t n 10 10 19.6 13 1437 941 10 0 50.4 7200 337882 315950
D C u t s n 10 10 19.6 1 1313 966 10 0 50.4 7200 360801 343056
SCF 10 3 19.6 5576 987720 −1 10 0 51.5 7200 1815207 −1
S C F t 10 9 19.6 1354 513872 −1 10 5 50.0 3823 3081605 −1
S C F t n 10 10 19.6 31 5160 −1 10 8 49.9 1508 800971 −1
S C F n 10 10 19.6 49 9415 −1 10 0 50.6 7200 894051 −1
0.2 EC 10 1 15.1 7099 208082 117362 10 0 45.1 7200 62300 63102
E C t 10 10 14.8 675 54742 23790 10 4 36.5 6326 138547 137549
E C t n 10 10 14.8 344 36386 16745 10 2 37.1 6450 120465 121687
E C n 10 2 15.3 6369 136657 94927 10 0 46.0 7200 40163 41557
E C s n 10 4 14.8 4894 231148 95062 10 0 39.2 7200 65167 63256
DCut 10 0 16.3 7200 48073 35316 10 0 38.9 7200 119789 87861
D C u t t 10 6 14.8 3196 55169 37144 10 6 35.8 3706 61762 47626
D C u t t n 10 10 14.8 835 13677 8698 10 7 35.8 2432 36099 27852
D C u t n 10 0 15.7 7200 39132 29700 10 0 38.5 7200 48576 40239
D C u t s n 10 1 15.6 7134 78339 57546 10 0 38.0 7200 88645 73235
SCF 10 0 17.0 7200 14435 −1 10 0 40.5 7200 39472 −1
S C F t 10 0 15.5 7200 173479 −1 10 0 37.8 7200 480980 −1
S C F t n 10 9 14.8 2401 31073 −1 10 1 36.1 6495 152260 −1
S C F n 10 0 15.2 7200 63078 −1 10 0 38.4 7200 29479 −1
0.5 EC 10 0 15.8 7200 69554 36260 10 0 38.8 7200 54153 55751
E C t 10 8 13.3 2570 62487 30425 10 5 30.7 4064 51442 50552
E C t n 9 8 13.2 1400 34106 18769 10 4 31.0 5038 59605 57375
E C n 10 0 16.2 7200 35944 18323 10 0 38.9 7200 28984 31127
E C s n 10 0 13.7 7200 296782 88962 10 0 33.8 7200 63430 64801
DCut 10 0 15.4 7200 7645 4291 10 0 36.0 7200 31008 19324
D C u t t 10 6 13.5 5152 9463 9036 10 6 30.3 4331 16003 13285
D C u t t n 10 5 13.5 4557 9195 8543 10 7 30.2 3552 12337 9780
D C u t n 10 0 15.4 7200 5807 3785 10 0 36.6 7200 6935 5131
D C u t s n 10 0 14.4 7200 12834 8154 10 0 32.4 7200 14108 9913
SCF 10 0 16.4 7200 1345 −1 10 0 34.5 7200 3160 −1
S C F t 10 0 14.6 7200 19313 −1 10 0 32.3 7200 35869 −1
S C F t n 10 5 13.5 4756 9842 −1 10 2 30.7 5842 16960 −1
S C F n 10 0 14.5 7200 6765 −1 10 0 33.1 7200 2327 −1