Advances in Operations Research

Research Article

Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

Table 4

Comparison of selected variants of formulations EC, DCut and SCF on the instances from SET-II.
| 𝐿 | = 5 | 𝐿 | = 1 0 | 𝐿 | = 2 0
| 𝑉 | , | 𝐸 | alg cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts
200, 800 EC 10 10 3.0 0 1 0 10 10 5.0 0 3 010 10 7.9 0 13 2
E C t 10 10 3.0 0 2 236 10 10 5.0 0 8 315 10 10 7.9 2 47 582
E C t n 10 10 3.0 0 2 157 10 10 5.0 0 6 249 10 10 7.9 1 20 515
E C n 10 10 3.0 0 1 0 10 10 5.0 0 1 010 10 7.9 0 6 2
E C s n 10 10 3.0 0 1 0 10 10 5.0 0 1 0 10 10 7.9 0 6 1
DCut 10 10 3.0 1 6 38 10 10 5.0 4 14 63 10 10 7.9 14 127 171
D C u t t 10 10 3.0 3 6 26 10 10 5.0 7 18 37 10 10 7.9 18 161 173
D C u t t n 10 10 3.0 0 4 29 10 10 5.0 2 7 36 10 10 7.9 8 21 63
D C u t n 10 10 3.0 0 2 24 10 10 5.0 0 6 49 10 10 5.0 0 6 49
D C u t s n 10 10 3.0 0 1 0 10 10 5.0 0 1 0 10 10 7.9 0 6 1
SCF 10 10 3.0 2 2 −1 10 10 5.0 9 32 −1 10 10 7.9 69 800 −1
S C F t 10 10 3.0 3 2 −1 10 10 5.0 9 32 −1 10 10 7.9 71 800 −1
S C F t n 10 10 3.0 0 1 −1 10 10 5.0 1 3 −1 10 10 7.9 6 16 −1
S C F n 10 10 3.0 0 1 −1 10 10 5.0 1 3 −1 10 10 7.9 6 16 −1
500, 2000 EC 10 10 3.5 0 1 0 10 10 5.9 0 2 0 10 10 9.9 0 12 0
E C t 10 10 3.5 3 2 621 10 10 5.9 6 7 833 10 10 9.9 16 44 1129
E C t n 10 10 3.5 2 1 541 10 10 5.9 5 6 763 10 10 9.9 16 25 1385
E C n 10 10 3.5 0 1 0 10 10 5.9 0 1 0 10 10 9.9 0 8 0
E C s n 10 10 3.5 0 1 0 10 10 3.5 0 1 0 10 10 9.9 0 7 0
DCut 10 10 3.5 5 5 34 10 10 5.9 14 14 76 10 10 9.9 48 152 184
D C u t t 10 10 3.5 13 7 25 10 10 5.9 28 15 34 10 10 9.9 68 181 144
D C u t t n 10 10 3.5 2 3 16 10 10 5.9 9 8 33 10 10 5.9 9 8 33
D C u t n 10 10 3.5 1 2 46 10 10 5.9 3 6 67 10 10 9.9 20 20 139
D C u t s n 10 10 3.5 1 2 82 10 10 5.9 3 6 60 10 10 9.9 20 19 129
SCF 10 10 3.5 10 3 −1 10 10 5.9 28 18 −1 10 10 9.9 372 661 −1
S C F t 10 10 3.5 11 3 −1 10 10 5.9 29 18 −1 10 10 9.9 384 661 −1
S C F t n 10 10 3.5 0 1 −1 10 10 5.9 4 3 −1 10 10 9.9 20 20 −1
S C F n 10 10 3.5 0 1 −1 10 10 5.9 3 3 −1 10 10 9.9 18 20 −1
1000, 4000 EC 10 10 4.1 0 1 0 10 10 6.6 0 1 0 10 10 11.3 0 13 0
E C t 10 10 4.1 20 1 1182 10 10 6.6 46 6 1762 10 10 11.3 121 54 3514
E C t n 10 10 4.1 300 1 3823 10 10 6.6 234 6 2660 10 10 11.3 108 26 2909
E C n 10 10 4.1 0 1 0 10 10 6.6 0 1 0 10 10 11.3 0 7 0
E C s n 10 10 4.1 0 1 0 10 10 6.6 0 1 0 10 10 11.3 0 6 0
DCut 10 10 4.1 16 5 40 10 10 6.6 47 13 259 10 10 11.3 144 191 275
D C u t t 10 10 4.1 54 6 22 10 10 6.6 90 20 36 10 10 11.3 240 189 150
D C u t t n 10 10 4.1 7 3 23 10 10 6.6 26 7 26 10 10 11.3 103 36 47
D C u t n 10 10 4.1 12 1 184 10 10 6.6 13 5 195 10 10 11.3 64 26 355
D C u t s n 10 10 4.1 11 1 178 10 10 6.6 47 6 495 10 10 11.3 57 24 253
SCF 10 10 4.1 30 2 −1 10 10 6.6 99 14 −1 10 10 11.3 1243 416 −1
S C F t 10 10 4.1 31 2 −1 10 10 6.6 96 14 −1 10 10 11.3 1303 416 −1
S C F t n 10 10 4.1 1 1 −1 10 10 6.6 12 3 −1 10 10 11.3 52 31 −1
S C F n 10 10 4.1 1 1 −1 10 10 6.6 12 3 −1 10 10 11.3 48 31 −1