Advances in Operations Research

Research Article

Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

Table 2

Comparison of selected variants of formulations EC, DCut, and SCF on the instances from SET-I with | 𝑉 | = 1 0 0 .
| 𝐿 | = 5 0 | 𝐿 | = 1 0 0 | 𝐿 | = 1 2 5
𝑑 alg cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts
0.2 EC 10 10 6.7 7 234 6510 10 9.7 62 3876 1072 9 9 11.2 123 9365 2843
E C t 10 10 6.7 8 347 196 10 10 9.7 25 2482 414 9 9 11.2 34 3769 871
E C t n 10 10 6.7 4 100 17310 10 9.7 11 857 339 9 9 11.2 16 1401 402
E C n 10 10 6.7 0 24 3 10 10 9.7 9 1298 179 9 9 11.2 33 2648 594
E C s n 10 10 6.7 0 31 3 10 10 9.7 6 1127 34 9 9 11.2 12 2570 89
DCut 10 10 6.7 80 1167 691 10 10 9.7 1013 14378 7798 9 8 11.2 1470 19646 11403
D C u t t 10 10 6.7 125 1458 95410 10 9.7 478 6676 3919 9 9 11.2 740 10273 6450
D C u t t n 10 10 6.7 21 127 11610 10 9.7 86 1021 729 9 9 11.2 115 1426 1017
D C u t n 10 10 6.7 11 90 96 10 10 9.7 57 1157 599 9 9 11.2 176 3186 1868
D C u t s n 10 10 6.7 12 94 89 10 10 9.7 51 1190 516 9 9 11.2 129 3086 1536
SCF 10 2 6.8 7028 136930 −1 10 0 10.3 7200 19854 −1 9 0 12.4 7200 17296 −1
S C F t 10 1 6.7 7133 143226 −1 10 0 10.3 7200 101319 −1 9 0 11.7 7200 119683 −1
S C F t n 10 10 6.7 15 83 −1 10 10 9.7 67 673 −1 9 9 11.2 85 1033 −1
S C F n 10 10 6.7 15 83 −1 10 10 9.7 63 673 −1 9 9 11.2 84 1033 −1
0.5 EC 10 10 3.0 17 46 5 10 10 4.7 374 5584 282 10 10 5.2 446 5307 630
E C t 10 10 3.0 14 69 148 10 10 4.7 175 5039 330 10 10 5.2 129 3249 382
E C t n 10 10 3.0 9 7 136 10 10 4.7 34 524 165 10 10 5.2 39 452 277
E C n 10 10 3.0 0 2 0 10 10 4.7 8 221 4 10 10 5.2 9 127 4
E C s n 10 10 3.0 0 2 0 10 10 4.7 9 173 4 10 10 5.2 11 370 12
DCut 10 10 3.0 217 488 272 10 8 4.8 3858 15810 7214 10 10 5.2 3150 9316 4187
D C u t t 10 10 3.0 190 465 256 10 9 4.7 3471 11770 6246 10 10 5.2 1794 5366 3175
D C u t t n 10 10 3.0 56 13 28 10 10 4.7 401 1133 450 10 10 5.2 305 633 342
D C u t n 10 10 3.0 27 12 28 10 10 4.7 261 1597 518 10 10 5.2 250 1179 401
D C u t s n 10 10 3.0 27 23 55 10 10 4.7 216 1539 390 10 10 5.2 225 1234 362
SCF 10 10 3.0 850 1475 −1 10 0 5.0 7200 11453 −1 10 0 5.8 7200 7586 −1
S C F t 10 10 3.0 722 1597 −1 10 6 4.7 5319 23618 −1 10 0 5.5 7200 18169 −1
S C F t n 10 10 3.0 22 1 −1 10 10 4.7 211 617 −1 10 10 5.2 171 298 −1
S C F n 10 10 3.0 20 1 −1 10 10 4.7 203 617 −1 10 10 5.2 176 298 −1
0.8 EC 10 10 2.0 12 2 12 10 10 3.0 161 848 98 10 10 4.0 999 4310 20
E C t 10 10 2.0 11 7 196 10 10 3.0 36 142 179 10 10 4.0 135 2344 130
E C t n 10 10 2.0 14 4 102 10 10 3.0 24 11 187 10 10 4.0 44 394 83
E C n 10 10 2.0 0 1 0 10 10 3.0 1 3 2 10 10 4.0 17 102 0
E C s n 10 10 2.0 0 1 0 10 10 3.0 2 4 1 10 10 4.0 17 51 0
DCut 10 10 2.0 255 97 65 10 9 3.1 2367 2440 1286 10 0 4.0 7200 6958 3525
D C u t t 10 10 2.0 198 127 131 10 9 3.1 1997 2702 1635 10 9 4.0 5083 6363 3410
D C u t t n 10 10 2.0 87 7 19 10 10 3.0 314 370 216 10 10 4.0 923 1193 408
D C u t n 10 10 2.0 40 5 22 10 10 3.0 418 932 457 10 10 4.0 780 1853 546
D C u t s n 10 10 2.0 33 3 29 10 10 3.0 128 161 93 10 10 4.0 740 2154 668
SCF 10 10 2.0 274 103 −1 10 0 3.6 7200 2826 −1 10 0 4.0 7200 2752 −1
S C F t 10 10 2.0 33 5 −1 10 0 4.0 7200 3035 −1 10 0 4.0 7200 2849 −1
S C F t n 10 10 2.0 28 1 −1 10 10 3.0 29 2 −1 10 10 4.0 243 349 −1
S C F n 10 10 2.0 28 1 −1 10 10 3.0 29 2 −1 10 10 4.0 230 349 −1