Advances in Operations Research

Research Article

Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

Table 6

Comparison of selected variants of formulations EC, DCut and SCF on the instances from SET-III with | 𝑉 | = 1 0 0 , 𝑎 ∈ { 2 , 5 } .
| 𝐿 | = 1 / 4 ⋅ | 𝐸 | , 𝑎 = 2 | 𝐿 | = 3 / 4 ⋅ | 𝐸 | , 𝑎 = 2 | 𝐿 | = 1 / 4 ⋅ | 𝐸 | , 𝑎 = 5 | 𝐿 | = 3 / 4 ⋅ | 𝐸 | , 𝑎 = 5
𝑑 alg cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts
0.05 EC 10 10 16.6 7 3222 3277 10 0 42.8 7200 112158 123363 10 10 10.5 0 152 452 10 0 21.4 7200 111275 106501
E C t 10 10 16.6 63 11657 9901 10 7 35.0 2558 113102 106934 10 10 10.5 0 362 400 10 4 20.8 4763 178547 160611
E C t n 10 10 16.6 12 4707 4080 10 7 35.0 2375 102179 93532 10 10 10.5 0 306 359 10 6 20.6 3467 143690 125295
E C n 10 10 16.6 2 1883 1956 10 0 42.4 7200 116472 124838 10 10 10.5 0 158 426 10 0 21.5 7200 107718 103093
DCut 10 10 16.6 31 4173 2409 10 0 35.1 7200 374197 286064 10 10 10.5 7 247 238 10 0 20.5 7200 375009 236293
D C u t t 10 10 16.6 36 3523 2114 10 10 34.7 112 6725 4842 10 10 10.5 10 350 301 10 9 20.5 1066 75587 46230
D C u t t n 10 10 16.6 16 1162 787 10 10 34.7 61 4661 3696 10 10 10.5 5 115 134 10 10 20.5 698 45870 25073
D C u t n 10 10 16.6 11 1026 694 10 0 35.0 7200 376389 268567 10 10 10.5 3 95 115 10 7 20.5 4126 215290 129837
SCF 10 1 16.7 7153 896512 −1 10 0 37.1 7200 701281 −1 10 9 10.5 2318 507224 −1 10 0 21.8 7200 276624 −1
S C F t 10 7 16.6 4038 1339695 −1 10 1 35.0 7046 3581766 −1 10 10 10.5 1580 440888 −1 10 0 21.0 7200 1707957 −1
S C F t n 10 10 16.6 29 3894 −1 10 10 34.7 609 239014 −1 10 10 10.5 4 284 −1 10 9 20.5 2218 462195 −1
S C F n 10 10 16.6 67 11755 −1 10 0 35.8 7200 666248 −1 10 10 10.5 5 329 −1 10 0 20.9 7200 720521 −1
0.2 EC 10 3 12.3 6521 268240 117079 10 0 31.8 7200 72720 69345 10 10 7.8 3364 236585 34987 10 0 19.5 7200 159231 107082
E C t 10 8 12.1 1840 81598 40109 10 3 26.2 5845 141568 127229 10 10 7.8 265 39875 773 10 3 15.1 5184 171490 89976
E C t n 10 10 11.9 629 42052 20637 10 3 26.3 5242 119550 107358 10 10 7.8 128 12441 651 10 3 15.1 5140 139983 90176
E C n 10 7 12.1 4285 166054 79457 10 0 34.0 7200 49859 50940 10 10 7.8 1041 56147 8166 10 0 19.0 7200 115188 89434
DCut 10 0 13.4 7200 43412 32497 10 0 27.3 7200 72779 48772 10 1 7.9 6892 70690 36507 10 0 16.6 7200 33350 23851
D C u t t 10 10 11.9 1477 17841 13183 10 7 25.6 2957 55433 38121 10 5 7.8 5653 67754 42560 10 4 14.9 5423 55800 43216
D C u t t n 10 10 11.9 681 5906 5180 10 9 25.6 1489 24931 17663 10 10 7.8 1628 15222 9552 10 6 14.8 4406 44628 32312
D C u t n 10 0 13.2 7200 39599 30225 10 0 27.4 7200 31085 23420 10 7 7.8 4679 65415 25812 10 0 15.8 7200 15761 11375
SCF 10 0 14.3 7200 13282 −1 10 0 30.0 7200 19389 −1 10 0 8.8 7200 22933 −1 10 0 18.1 7200 12399 −1
S C F t 10 0 12.9 7200 105555 −1 10 0 27.0 7200 320786 −1 10 0 8.1 7200 107916 −1 10 0 15.8 7200 109149 −1
S C F t n 10 8 12.1 1909 18528 −1 10 4 25.9 5338 87496 −1 10 10 7.8 1669 11756 −1 10 2 15.1 6327 44397 −1
S C F n 10 0 12.8 7200 47542 −1 10 0 27.6 7200 15439 −1 10 9 7.8 4151 59801 −1 10 0 16.0 7200 10494 −1
0.5 EC 10 0 11.5 7200 98257 38000 10 0 28.4 7200 93989 77494 10 1 6.9 6785 101172 7242 10 0 14.5 7200 50518 29040
E C t 10 10 10.9 632 42951 5268 10 1 23.4 6487 85485 71003 10 10 6.9 612 27936 785 9 5 13.1 3804 100666 38284
E C t n 10 10 10.9 506 22467 6432 10 3 26.3 5242 119550 107358 10 10 6.9 255 6604 532 9 6 13.0 3472 72582 38165
E C n 10 0 11.3 7200 37858 18365 10 0 29.0 7200 44406 39926 10 0 7.0 7200 29141 2143 10 0 16.2 7200 11751 6165
DCut 10 0 11.8 7200 9769 5503 10 0 30.4 7200 15852 9516 10 0 7.1 7200 11487 5995 10 0 15.2 7200 5742 3186
D C u t t 10 0 11.3 7200 13089 11560 10 8 22.5 4745 9585 8851 10 0 7.4 7200 7977 6213 10 0 13.8 7200 7827 7958
D C u t t n 10 5 11.2 5664 11813 9786 10 5 22.8 4259 8850 8481 10 6 7.1 5089 5318 3529 10 4 13.1 5743 7934 7389
D C u t n 10 0 11.9 7200 7129 4426 10 0 27.1 7200 4738 2996 10 1 7.1 6717 7337 3172 10 0 15.2 7200 2682 1652
SCF 10 0 13.2 7200 1477 −1 10 0 26.8 7200 1628 −1 10 0 8.0 7200 2606 −1 10 0 16.2 7200 923 −1
S C F t 10 0 12.1 7200 13970 −1 10 0 24.3 7200 26439 −1 10 0 7.6 7200 6757 −1 10 0 14.3 7200 10634 −1
S C F t n 10 6 10.9 4841 6975 −1 10 0 23.4 7200 12529 −1 10 7 7.0 4238 3003 −1 10 2 13.3 5923 6203 −1
S C F n 10 0 11.8 7200 9232 −1 10 0 25.0 7200 3000 −1 10 0 7.0 7200 21470 −1 10 0 14.4 7200 4668 −1