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 ; .
| | | | | | | | alg | | cnt | opt | obj | | bbn | cuts | | cnt | opt | obj | | bbn | cuts |
| 0.05 | EC | | 10 | 10 | 19.6 | 2 | 1892 | 1722 | | 10 | 0 | 61.6 | 7200 | 108393 | 124719 | | | 10 | 10 | 19.6 | 23 | 6887 | 6026 | | 10 | 1 | 51.3 | 6480 | 178187 | 195559 | | | 10 | 10 | 19.6 | 14 | 4944 | 4486 | | 10 | 2 | 51.2 | 5760 | 163875 | 182801 | | | 10 | 10 | 19.6 | 2 | 1491 | 1246 | | 10 | 0 | 62.5 | 7200 | 103413 | 119245 | | | 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 | | | 10 | 10 | 19.6 | 34 | 4174 | 2487 | | 10 | 4 | 49.8 | 4381 | 76629 | 55867 | | | 10 | 10 | 19.6 | 12 | 1148 | 759 | | 10 | 6 | 49.8 | 3195 | 87152 | 60318 | | | 10 | 10 | 19.6 | 13 | 1437 | 941 | | 10 | 0 | 50.4 | 7200 | 337882 | 315950 | | | 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 | | | 10 | 9 | 19.6 | 1354 | 513872 | −1 | | 10 | 5 | 50.0 | 3823 | 3081605 | −1 | | | 10 | 10 | 19.6 | 31 | 5160 | −1 | | 10 | 8 | 49.9 | 1508 | 800971 | −1 | | | 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 | | | 10 | 10 | 14.8 | 675 | 54742 | 23790 | | 10 | 4 | 36.5 | 6326 | 138547 | 137549 | | | 10 | 10 | 14.8 | 344 | 36386 | 16745 | | 10 | 2 | 37.1 | 6450 | 120465 | 121687 | | | 10 | 2 | 15.3 | 6369 | 136657 | 94927 | | 10 | 0 | 46.0 | 7200 | 40163 | 41557 | | | 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 | | | 10 | 6 | 14.8 | 3196 | 55169 | 37144 | | 10 | 6 | 35.8 | 3706 | 61762 | 47626 | | | 10 | 10 | 14.8 | 835 | 13677 | 8698 | | 10 | 7 | 35.8 | 2432 | 36099 | 27852 | | | 10 | 0 | 15.7 | 7200 | 39132 | 29700 | | 10 | 0 | 38.5 | 7200 | 48576 | 40239 | | | 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 | | | 10 | 0 | 15.5 | 7200 | 173479 | −1 | | 10 | 0 | 37.8 | 7200 | 480980 | −1 | | | 10 | 9 | 14.8 | 2401 | 31073 | −1 | | 10 | 1 | 36.1 | 6495 | 152260 | −1 | | | 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 | | | 10 | 8 | 13.3 | 2570 | 62487 | 30425 | | 10 | 5 | 30.7 | 4064 | 51442 | 50552 | | | 9 | 8 | 13.2 | 1400 | 34106 | 18769 | | 10 | 4 | 31.0 | 5038 | 59605 | 57375 | | | 10 | 0 | 16.2 | 7200 | 35944 | 18323 | | 10 | 0 | 38.9 | 7200 | 28984 | 31127 | | | 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 | | | 10 | 6 | 13.5 | 5152 | 9463 | 9036 | | 10 | 6 | 30.3 | 4331 | 16003 | 13285 | | | 10 | 5 | 13.5 | 4557 | 9195 | 8543 | | 10 | 7 | 30.2 | 3552 | 12337 | 9780 | | | 10 | 0 | 15.4 | 7200 | 5807 | 3785 | | 10 | 0 | 36.6 | 7200 | 6935 | 5131 | | | 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 | | | 10 | 0 | 14.6 | 7200 | 19313 | −1 | | 10 | 0 | 32.3 | 7200 | 35869 | −1 | | | 10 | 5 | 13.5 | 4756 | 9842 | −1 | | 10 | 2 | 30.7 | 5842 | 16960 | −1 | | | 10 | 0 | 14.5 | 7200 | 6765 | −1 | | 10 | 0 | 33.1 | 7200 | 2327 | −1 |
|
|