Advances in Operations Research

Research Article

Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

Table 7

Comparison of selected variants of formulations EC, DCut and SCF on the grid graph instances from SET-III with | 𝐸 | ≈ 4 ⋅ | 𝑉 | .
| 𝑉 | = 1 0 × 1 0 | 𝑉 | = 2 0 × 2 0
| 𝐿 | alg cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts
30 EC 10 10 9.2 4 2041 1540 10 10 11.5 61 7496 400
E C t 10 10 9.2 6 2641 1843 10 10 11.5 183 7547 5819
E C t n 10 10 9.2 4 1639 1544 10 10 11.5 91 3757 4231
E C n 10 10 9.2 1 1369 656 10 10 11.5 17 3602 200
E C s n 10 10 9.2 1 1281 601 10 10 11.5 17 3558 175
DCut 10 10 9.2 61 4948 3240 2 2 11.0 5224 6233 37505
D C u t t 10 10 9.2 93 6196 4135 10 10 11.5 3029 22956 19238
D C u t t n 10 10 9.2 34 1892 1710 10 10 11.5 627 4058 10961
D C u t n 10 10 9.2 18 1512 1364 1 0 12.0 7200 39 24766
D C u t s n 10 10 9.2 19 1356 2314 1 0 13.0 7200 26 23113
SCF 10 10 9.2 815 118270 −1 10 0 11.8 7200 22192 −1
S C F t 10 10 9.2 641 90448 −1 10 0 11.7 7200 22091 −1
S C F t n 10 10 9.2 17 1280 −1 10 10 11.5 251 3127 −1
S C F n 10 10 9.2 12 1008 −1 10 10 11.5 218 3076 −1
50 EC 9 8 13.0 1018 54653 41036 10 9 17.1 4341 464602 31132
E C t 9 7 13.1 1959 99397 73687 10 0 17.0 7200 301858 167539
E C t n 9 8 13.0 1578 83996 67834 10 10 17.0 3834 212265 107170
E C n 9 9 12.9 129 25299 16378 10 10 17.0 1347 208221 11217
E C s n 9 9 12.9 66 22339 13131 10 10 17.0 1087 193213 8470
DCut 9 9 12.9 867 67360 37873 7 0 17.3 7200 29390 47832
D C u t t 9 9 12.9 1032 74718 42088 10 0 17.2 7200 32248 33668
D C u t t n 9 9 12.9 302 20596 12907 10 0 17.0 7200 86172 64236
D C u t n 9 9 12.9 336 28974 17613 7 0 16.3 7200 3345 36785
D C u t s n 9 9 12.9 207 20951 13323 7 0 15.7 7200 648 23682
SCF 9 0 13.3 7200 368322 −1 10 0 18.5 7200 13103 −1
S C F t 9 0 13.2 7200 741954 −1 10 0 18.5 7200 19592 −1
S C F t n 9 9 12.9 215 21632 −1 10 0 17.1 7200 131296 −1
S C F n 9 9 12.9 299 34004 −1 10 8 17.1 5532 169723 −1
80 EC 10 0 19.5 7200 134608 118377 10 0 25.0 7200 199143 139246
E C t 10 0 19.9 7200 231789 208661 10 0 24.9 7200 143214 104486
E C t n 10 0 19.6 7200 229619 202787 10 0 24.8 7200 146616 112030
E C n 10 0 19.5 7200 162192 138904 10 0 24.6 7200 305748 138953
E C s n 10 0 18.9 7200 228167 176741 10 0 24.6 7200 299188 134344
DCut 10 0 18.8 7200 252826 225273 10 0 25.5 7200 31756 32402
D C u t t 10 0 18.9 7200 248123 216513 9 0 19.8 7200 24121 25391
D C u t t n 9 0 18.7 7200 283625 220940 10 0 25.2 7200 43604 44755
D C u t n 10 0 18.8 7200 239489 197073 8 0 24.6 7200 54226 62124
D C u t s n 10 0 18.9 7200 248966 213157 7 0 25.1 7200 25262 46754
SCF 10 0 19.7 7200 285092 −1 10 0 27.0 7200 9767 −1
S C F t 10 0 19.2 7200 948572 −1 10 0 28.0 7200 22180 −1
S C F t n 10 0 19.0 7200 689593 −1 10 0 25.3 7200 68435 −1
S C F n 10 0 18.8 7200 863039 −1 10 0 25.2 7200 99643 −1