Advances in Operations Research

Research Article

Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

Table 8

Comparison of formulations šø š¶ š‘” and š· š¶ š‘¢ š‘” š‘” with Inequalities (3.22), indicated with index š‘› , and with additional Inequalities (3.23), indicated with index Ģƒ š‘› .
E C t n / D C u t t n E C t Ģƒ n / D C u t t Ģƒ n
| š‘‰ | , | šø | , š‘Ž , | šæ | cnt opt obj š‘” bbn cuts cnt opt obj š‘” bbn cuts
1 0 0 , 2 4 7 , 1 , 6 1 10 10 19.6 14 4944 4486 10 10 19.6 0 499 492
10 10 19.6 12 1148 759 10 10 19.6 19 1577 1034
1 0 0 , 2 4 7 , 1 , 1 8 5 10 2 51.2 5760 163875 182801 10 7 50.0 2174 65781 68723
10 6 49.8 3195 87152 6031810 5 49.8 4284 86769 62183
1 0 0 , 9 0 0 , 1 , 2 4 7 10 10 14.8 344 36386 16745 10 10 14.8 177 18352 6741
10 10 14.8 835 13677 869810 10 14.8 1949 26973 16494
1 0 0 , 9 0 0 , 1 , 7 4 2 10 2 37.1 6450 120465 121687 10 7 35.8 2403 48038 45398
10 7 35.8 2432 36099 27852 10 8 35.7 1822 20522 15153
1 0 0 , 2 4 7 5 , 1 , 6 1 8 10 8 13.2 1400 34106 187699 8 13.2 1801 46469 22363
10 5 13.5 4557 9195 8543 10 4 13.6 5417 10773 9933
1 0 0 , 2 4 7 5 , 1 , 1 8 5 6 10 4 31.0 5038 59605 57375 10 7 30.3 2506 27241 24957
10 7 30.2 3552 12337 9780 10 8 30.2 2907 3715 3689
1 0 0 , 2 4 7 , 2 , 6 1 10 10 16.6 12 4707 4080 10 10 16.6 1 601 498
10 10 16.6 16 1162 787 10 10 16.6 21 1348 907
1 0 0 , 2 4 7 , 2 , 1 8 5 10 7 35.0 2375 102179 93532 10 10 34.7 9 3269 3274
10 10 34.7 61 4661 3696 10 10 34.7 19 1425 1226
1 0 0 , 9 0 0 , 2 , 2 4 7 10 10 11.9 629 42052 20637 10 10 11.9 912 55106 20864
10 10 11.9 681 5906 5180 10 10 11.9 1523 16435 12011
1 0 0 , 9 0 0 , 2 , 7 4 2 10 3 26.3 5242 119550 107358 10 7 25.8 3265 69685 53785
10 9 25.6 1489 24931 17663 10 9 25.6 1583 17076 12240
1 0 0 , 2 4 7 5 , 2 , 6 1 8 10 10 10.9 506 22467 6432 10 10 10.9 558 37153 3921
10 5 11.2 5664 11813 978610 1 11.7 7050 12503 11444
1 0 0 , 2 4 7 5 , 2 , 1 8 5 6 10 4 23.2 5213 61908 53294 10 3 23.2 5757 73145 57657
10 5 22.8 4259 8850 8481 10 8 22.5 3649 4185 4254
1 0 0 , 2 4 7 , 5 , 6 1 10 10 10.5 0 306 359 10 10 10.5 0 248 306
10 10 10.5 5 115 13410 10 10.5 11 316 321
1 0 0 , 2 4 7 , 5 , 1 8 5 10 6 20.6 3467 143690 125295 10 9 20.5 1202 60571 49983
10 10 20.5 698 45870 25073 10 10 20.5 498 36774 20977
1 0 0 , 9 0 0 , 5 , 2 4 7 10 10 7.8 128 12441 65110 10 7.8 288 39324 825
10 10 7.8 1628 15222 9552 10 5 7.8 5675 66499 42125
1 0 0 , 9 0 0 , 5 , 7 4 2 10 3 15.1 5140 139983 90176 9 4 15.0 4344 155589 73198
10 6 14.8 4406 44628 32312 10 4 14.9 5171 50434 38692
1 0 0 , 2 4 7 5 , 5 , 6 1 8 10 10 6.9 255 6604 532 10 10 6.9 624 27936 785
10 6 7.1 5089 5318 3529 10 0 7.4 7200 8303 6431
1 0 0 , 2 4 7 5 , 5 , 1 8 5 6 10 6 13.0 3472 72582 38165 10 6 13.0 3848 103635 41651
10 4 13.1 5743 7934 7389 10 1 13.6 7191 8419 8617
1 0 Ɨ 1 0 , 3 6 0 , 1 , 3 0 10 10 9.2 4 1639 1544 10 10 9.2 6 2641 1843
10 10 9.2 34 1892 1710 10 10 9.2 90 6196 4135
1 0 Ɨ 1 0 , 3 6 0 , 1 , 5 0 9 8 13.0 1578 83996 67834 9 8 13.0 1877 102421 75692
9 9 12.9 302 20596 12907 9 9 12.9 1034 74718 42088
1 0 Ɨ 1 0 , 3 6 0 , 1 , 8 0 10 0 19.6 7200 229619 202787 10 0 19.9 7200 251957 226941
10 0 18.7 7200 283625 220940 9 0 18.8 7200 283288 241399
2 0 Ɨ 2 0 , 1 5 2 0 , 1 , 3 0 10 10 11.5 91 3757 423110 10 11.5 176 7547 5819
10 10 11.5 627 4058 10961 10 10 11.5 2866 22956 19238
2 0 Ɨ 2 0 , 1 5 2 0 , 1 , 5 0 10 10 17.0 3834 212265 10717010 1 17.0 7194 326051 178058
10 0 17.0 7200 86172 64236 10 0 17.2 7200 34742 35779
2 0 Ɨ 2 0 , 1 5 2 0 , 1 , 8 0 10 0 24.8 7200 146616 112030 10 0 24.9 7200 150529 110120
10 0 25.2 7200 43604 44755 10 0 20.6 7200 25718 26997