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.
| | | | | | | | | , | alg | | cnt | opt | obj | | bbn | cuts | | cnt | opt | obj | | bbn | cuts | | cnt | opt | obj | | bbn | cuts |
| 200, 800 | EC | | 10 | 10 | 3.0 | 0 | 1 | 0 | | 10 | 10 | 5.0 | 0 | 3 | 0 | | 10 | 10 | 7.9 | 0 | 13 | 2 | | | 10 | 10 | 3.0 | 0 | 2 | 236 | | 10 | 10 | 5.0 | 0 | 8 | 315 | | 10 | 10 | 7.9 | 2 | 47 | 582 | | | 10 | 10 | 3.0 | 0 | 2 | 157 | | 10 | 10 | 5.0 | 0 | 6 | 249 | | 10 | 10 | 7.9 | 1 | 20 | 515 | | | 10 | 10 | 3.0 | 0 | 1 | 0 | | 10 | 10 | 5.0 | 0 | 1 | 0 | | 10 | 10 | 7.9 | 0 | 6 | 2 | | | 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 | | | 10 | 10 | 3.0 | 3 | 6 | 26 | | 10 | 10 | 5.0 | 7 | 18 | 37 | | 10 | 10 | 7.9 | 18 | 161 | 173 | | | 10 | 10 | 3.0 | 0 | 4 | 29 | | 10 | 10 | 5.0 | 2 | 7 | 36 | | 10 | 10 | 7.9 | 8 | 21 | 63 | | | 10 | 10 | 3.0 | 0 | 2 | 24 | | 10 | 10 | 5.0 | 0 | 6 | 49 | | 10 | 10 | 5.0 | 0 | 6 | 49 | | | 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 | | | 10 | 10 | 3.0 | 3 | 2 | −1 | | 10 | 10 | 5.0 | 9 | 32 | −1 | | 10 | 10 | 7.9 | 71 | 800 | −1 | | | 10 | 10 | 3.0 | 0 | 1 | −1 | | 10 | 10 | 5.0 | 1 | 3 | −1 | | 10 | 10 | 7.9 | 6 | 16 | −1 | | | 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 | | | 10 | 10 | 3.5 | 3 | 2 | 621 | | 10 | 10 | 5.9 | 6 | 7 | 833 | | 10 | 10 | 9.9 | 16 | 44 | 1129 | | | 10 | 10 | 3.5 | 2 | 1 | 541 | | 10 | 10 | 5.9 | 5 | 6 | 763 | | 10 | 10 | 9.9 | 16 | 25 | 1385 | | | 10 | 10 | 3.5 | 0 | 1 | 0 | | 10 | 10 | 5.9 | 0 | 1 | 0 | | 10 | 10 | 9.9 | 0 | 8 | 0 | | | 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 | | | 10 | 10 | 3.5 | 13 | 7 | 25 | | 10 | 10 | 5.9 | 28 | 15 | 34 | | 10 | 10 | 9.9 | 68 | 181 | 144 | | | 10 | 10 | 3.5 | 2 | 3 | 16 | | 10 | 10 | 5.9 | 9 | 8 | 33 | | 10 | 10 | 5.9 | 9 | 8 | 33 | | | 10 | 10 | 3.5 | 1 | 2 | 46 | | 10 | 10 | 5.9 | 3 | 6 | 67 | | 10 | 10 | 9.9 | 20 | 20 | 139 | | | 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 | | | 10 | 10 | 3.5 | 11 | 3 | −1 | | 10 | 10 | 5.9 | 29 | 18 | −1 | | 10 | 10 | 9.9 | 384 | 661 | −1 | | | 10 | 10 | 3.5 | 0 | 1 | −1 | | 10 | 10 | 5.9 | 4 | 3 | −1 | | 10 | 10 | 9.9 | 20 | 20 | −1 | | | 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 | | | 10 | 10 | 4.1 | 20 | 1 | 1182 | | 10 | 10 | 6.6 | 46 | 6 | 1762 | | 10 | 10 | 11.3 | 121 | 54 | 3514 | | | 10 | 10 | 4.1 | 300 | 1 | 3823 | | 10 | 10 | 6.6 | 234 | 6 | 2660 | | 10 | 10 | 11.3 | 108 | 26 | 2909 | | | 10 | 10 | 4.1 | 0 | 1 | 0 | | 10 | 10 | 6.6 | 0 | 1 | 0 | | 10 | 10 | 11.3 | 0 | 7 | 0 | | | 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 | | | 10 | 10 | 4.1 | 54 | 6 | 22 | | 10 | 10 | 6.6 | 90 | 20 | 36 | | 10 | 10 | 11.3 | 240 | 189 | 150 | | | 10 | 10 | 4.1 | 7 | 3 | 23 | | 10 | 10 | 6.6 | 26 | 7 | 26 | | 10 | 10 | 11.3 | 103 | 36 | 47 | | | 10 | 10 | 4.1 | 12 | 1 | 184 | | 10 | 10 | 6.6 | 13 | 5 | 195 | | 10 | 10 | 11.3 | 64 | 26 | 355 | | | 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 | | | 10 | 10 | 4.1 | 31 | 2 | −1 | | 10 | 10 | 6.6 | 96 | 14 | −1 | | 10 | 10 | 11.3 | 1303 | 416 | −1 | | | 10 | 10 | 4.1 | 1 | 1 | −1 | | 10 | 10 | 6.6 | 12 | 3 | −1 | | 10 | 10 | 11.3 | 52 | 31 | −1 | | | 10 | 10 | 4.1 | 1 | 1 | −1 | | 10 | 10 | 6.6 | 12 | 3 | −1 | | 10 | 10 | 11.3 | 48 | 31 | −1 |
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