Advances in Operations Research

Research Article

Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

Table 3

Comparison of selected variants of formulations EC, DCut, and SCF on the instances from SET-I with | 𝑉 | = 2 0 0 .
| 𝐿 | = 1 0 0 | 𝐿 | = 2 0 0 | 𝐿 | = 2 5 0
𝑑 alg cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts
0.2 EC10 8 8.0 3770 52682 16621 10 0 12.9 7200 42289 22303 10 0 15.4 7200 32009 18669
E C t 10 7 8.0 4541 43756 7665 10 0 13.6 7200 43298 8007 10 0 16.0 7200 43792 7293
E C t n 10 10 7.9 1296 14254 539 10 2 13.3 6878 60643 1436 10 1 14.9 6761 46296 1658
E C n 10 10 7.9 201 8379 5 10 5 12.2 5146 189033 973 10 3 13.8 6387 144597 5207
E C s n 10 10 7.9 191 8322 4 10 7 12.1 4331 182237 81 10 3 13.9 6153 250129 158
DCut 10 0 8.8 7200 10929 897110 0 14.5 7200 3850 3632 10 0 18.9 7200 3681 3548
D C u t t 10 0 9.0 7200 4392 4036 10 0 14.5 7200 2896 2866 10 0 16.1 7200 2653 2622
D C u t t n 10 7 8.1 5487 13056 8036 10 0 13.0 7200 5588 4763 10 0 15.7 7200 3982 3552
D C u t n 10 9 8.0 3398 14653 8637 10 0 12.9 7200 15877 12200 10 0 14.9 7200 11207 9494
D C u t s n 10 9 8.0 2996 14937 7658 10 0 12.7 7200 19280 13569 10 0 14.7 7200 13712 10837
SCF 10 0 9.3 7200 1017 −1 10 0 14.5 7200 634 −110 0 16.8 7200 559 −1
S C F t 10 0 8.9 7200 3204 −1 10 0 13.5 7200 4733 −1 10 0 15.8 7200 5326 −1
S C F t n 10 8 8.0 3353 9362 −1 10 0 12.4 7200 6854 −1 10 0 14.1 7200 4343 −1
S C F n 10 8 8.0 3498 8308 −1 10 0 12.4 7200 6468 −1 10 0 14.1 7200 4099 −1
0.5 EC 10 10 3.4 769 2082 69 10 0 5.8 7200 8603 539 10 0 6.5 7200 5380 456
E C t 10 10 3.4 1452 2744 558 10 0 5.8 7200 10307 647 10 0 6.4 7200 9084 1024
E C t n 10 10 3.4 570 469 678 10 7 5.5 4249 6550 908 10 0 6.5 7200 15870 861
E C n 10 10 3.4 25 126 1 10 9 5.4 1291 14284 12 10 8 6.4 4323 57715 31
E C s n 10 10 3.4 19 92 1 10 9 5.4 1176 14653 6 10 9 6.4 4049 62371 18
DCut 9 0 4.1 7200 1086 728 10 0 7.2 7200 323 265 10 0 7.9 7200 272 215
D C u t t 9 0 4.3 7200 613 469 10 0 7.9 7200 298 290 10 0 8.2 7200 335 307
D C u t t n 10 8 3.5 5135 954 48110 0 6.6 7200 557 349 10 0 7.4 7200 420 282
D C u t n 10 8 3.5 3132 1079 507 10 0 6.2 7200 1795 92910 0 7.1 7200 1097 564
D C u t s n 10 9 3.4 2054 979 412 10 0 6.0 7200 2072 912 10 0 6.7 7200 1432 671
SCF 10 0 4.3 7200 124 −110 0 7.0 7200 69 −1 10 0 7.8 7200 54 −1
S C F t 10 0 3.9 7200 207 −1 10 0 6.5 7200 166 −1 10 0 7.3 7200 150 −1
S C F t n 10 10 3.4 1102 270 −1 10 0 5.7 7200 828 −1 10 0 6.5 7200 839 −1
S C F n 10 10 3.4 1204 270 −1 10 0 5.7 7200 749 −1 10 0 6.4 7200 728 −1
0.8 EC 10 10 2.6 2803 2968 16 10 0 4.0 7200 1132 16 10 0 5.0 7200 1640 48
E C t 10 10 2.6 3040 3650 50510 0 4.0 7200 2146 656 10 2 4.4 7064 6763 757
E C t n 10 9 2.7 2739 103 613 10 10 4.0 5038 6819 634 10 9 4.1 2902 1331 776
E C n 10 10 2.6 76 2 73 10 10 4.0 1122 5975 1 10 10 4.0 609 3324 3
E C s n 10 10 2.6 28 1 1 10 10 4.0 911 4845 1 10 10 4.0 301 777 1
DCut 4 0 3.0 7200 152 134 10 0 8.2 7201 105 110 10 0 7.1 7200 69 70
D C u t t 10 0 3.9 7200 151 171 10 0 5.2 7202 110 112 10 0 6.8 7200 111 112
D C u t t n 10 3 3.3 6344 142 67 10 0 4.6 7200 177 102 10 0 5.5 7200 120 98
D C u t n 10 3 2.7 6528 1103 444 10 0 4.2 7200 329 170 10 0 4.9 7200 158 126
D C u t s n 10 6 2.6 5135 799 292 10 0 4.0 7200 556 227 10 0 5.0 7200 226 140
SCF 10 0 2.9 7200 69 −110 0 4.9 7200 35 −1 10 0 5.5 7200 33 −1
S C F t 10 2 2.8 5923 54 −1 10 0 4.3 7200 58 −1 10 0 5.1 7201 35 −1
S C F t n 10 9 2.6 4177 74 −1 10 1 4.0 6929 391 −1 10 3 4.7 6712 264 −1
S C F n 10 9 2.6 4183 79 −1 10 1 4.0 6973 375 −1 10 2 4.7 6871 229 −1