Skip to main content

Table 8 Numbers of instances solved to optimality (\(\#_\mathrm{solved}\)), geometric means of CPU-times in seconds, and average optimality gaps in (%) with respect to \(D\) and \(D'\) for random instances

From: The two-level diameter constrained spanning tree problem

Inst \(D'\) \(D\) \(\#\) \(\#_\mathrm{solved}\) CPU-time (s) Gap (%)
     (2T) \(\mathrm {(2T)}^+\) (3dLG) (2T) \(\mathrm {(2T)}^+\) (3dLG) (2T) \(\mathrm {(2T)}^+\) (3dLG)
TR30 3 5 6 6 6 6 484 127 38 0.0 0.0 0.0
TR30 3 6 6 6 6 6 238 139 27 0.0 0.0 0.0
TR30 3 7 6 6 6 6 332 405 41 0.0 0.0 0.0
TR30 3 8 6 6 6 6 239 251 59 0.0 0.0 0.0
TR30 4 6 6 6 6 6 7 6 2 0.0 0.0 0.0
TR30 4 7 6 6 6 6 11 17 6 0.0 0.0 0.0
TR30 4 8 6 6 6 6 11 11 9 0.0 0.0 0.0
TR30 4 9 6 6 6 6 16 23 10 0.0 0.0 0.0
TR30 5 7 6 6 6 6 75 64 19 0.0 0.0 0.0
TR30 5 8 6 6 6 6 45 50 11 0.0 0.0 0.0
TR30 5 9 6 6 6 6 108 150 31 0.0 0.0 0.0
TR30 5 10 6 6 6 6 91 95 28 0.0 0.0 0.0
TR30 6 8 6 6 6 6 6 6 2 0.0 0.0 0.0
TR30 6 9 6 6 6 6 14 21 8 0.0 0.0 0.0
TR30 6 10 6 6 6 6 10 11 8 0.0 0.0 0.0
TR30 6 11 6 6 6 6 19 26 23 0.0 0.0 0.0
TR40 3 5 8 7 7 8 1,451 554 165 0.1 0.0 0.0
TR40 3 6 8 7 7 8 1,064 857 87 0.1 0.1 0.0
TR40 3 7 8 7 6 8 866 984 213 0.1 0.1 0.0
TR40 3 8 8 6 6 8 703 723 233 0.1 0.1 0.0
TR40 4 6 8 8 8 8 174 136 28 0.0 0.0 0.0
TR40 4 7 8 8 8 8 369 165 63 0.0 0.0 0.0
TR40 4 8 8 8 8 8 194 155 65 0.0 0.0 0.0
TR40 4 9 8 8 7 8 490 319 66 0.0 0.0 0.0
TR40 5 7 8 8 8 8 2,963 1,398 380 0.0 0.0 0.0
TR40 5 8 8 8 8 8 1,683 1,015 219 0.0 0.0 0.0
TR40 5 9 8 6 7 8 4,167 2,964 493 0.1 0.1 0.0
TR40 5 10 8 7 7 8 2,759 2,821 355 0.1 0.0 0.0
TR40 6 8 8 8 8 8 202 136 32 0.0 0.0 0.0
TR40 6 9 8 8 8 8 561 400 95 0.0 0.0 0.0
TR40 6 10 8 8 8 8 433 356 74 0.0 0.0 0.0
TR40 6 11 8 5 6 8 1,087 933 112 0.1 12.6 0.0
TR60 3 5 6 4 4 6 3,677 3,056 2,100 0.2 0.2 0.0
TR60 3 6 6 3 3 6 2,487 2,192 1,255 0.2 0.3 0.0
TR60 3 7 6 3 3 6 2,898 3,533 2,925 16.9 0.3 0.0
TR60 3 8 6 3 3 6 3,323 4,077 2,685 0.3 0.3 0.0
TR60 4 6 6 6 6 6 1,002 670 145 0.0 0.0 0.0
TR60 4 7 6 6 6 6 1,455 1,061 316 0.0 0.0 0.0
TR60 4 8 6 6 5 6 722 722 257 0.0 0.0 0.0
TR60 4 9 6 6 5 6 1,164 1,040 297 0.0 0.0 0.0
TR60 5 7 6 2 4 6 8,864 6,153 2,296 0.4 0.2 0.0
TR60 5 8 6 3 5 6 5,707 3,557 1,420 16.9 0.1 0.0
TR60 5 9 6 3 4 6 5,469 6,111 3,309 0.2 16.8 0.0
TR60 5 10 6 3 3 6 5,308 5,989 3,830 33.5 33.5 0.0
TR60 6 8 6 5 6 6 1,821 1,747 306 16.7 0.0 0.0
TR60 6 9 6 4 4 6 2,064 2,452 1,083 33.3 33.3 0.0
TR60 6 10 6 4 4 6 1,693 1,655 727 33.3 33.3 0.0
TR60 6 11 6 4 3 6 2,815 3,637 1,849 16.7 33.4 0.0
  1. Best values are marked in bold