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# Table 5 Results for solving the LP relaxations on instances with 31 and 41 nodes: numbers of instances solved within the given time limit (#$$_\mathrm{solved}$$), geometric means of CPU-times in seconds, and average LP gaps (%) with respect to instance graph and $$|P|$$

Inst $$|P|$$ $$\#$$ $$\#_\mathrm{solved}$$ CPU-time (s) Gap (%)
(2T) $$\mathrm {(2T)}^+$$ (3dLG) (2T) $$\mathrm {(2T)}^+$$ (3dLG) (2T) $$\mathrm {(2T)}^+$$ (3dLG)
TC30 5 16 16 16 16 41 33 198 0.1 0.1 0.4
TC30 10 16 16 16 16 88 84 121 0.1 0.1 0.1
TC30 15 16 16 16 16 320 168 109 0.3 0.1 0.1
TC30 20 16 16 16 16 191 153 83 0.5 0.3 0.0
TC30 25 16 14 16 16 636 335 90 0.3 0.1 0.0
TC30 30 16 16 16 16 275 341 87 0.0 0.0 0.0
TC40 5 16 16 16 16 393 304 2,205 0.1 0.1 0.5
TC40 10 16 16 16 16 303 285 607 0.1 0.1 0.2
TC40 15 16 16 16 16 832 433 497 0.4 0.1 0.2
TC40 20 16 15 16 16 993 486 417 0.6 0.2 0.2
TC40 25 16 15 16 16 1,318 1,021 364 0.6 0.2 0.2
TC40 30 16 14 15 16 2,005 1,251 437 0.3 0.1 0.1
TC40 35 16 13 15 16 1,776 1,692 420 0.1 0.0 0.1
TC40 40 16 15 13 16 2,154 2,518 617 0.0 0.0 0.0
TR30 5 16 16 16 16 11 7 26 1.1 0.4 0.3
TR30 10 16 16 16 16 33 23 59 1.2 0.3 0.2
TR30 15 16 16 16 16 99 56 68 0.2 0.1 0.1
TR30 20 16 16 16 16 85 59 59 0.0 0.0 0.0
TR30 25 16 16 16 16 206 181 71 0.1 0.0 0.0
TR30 30 16 16 16 16 201 233 62 0.0 0.0 0.0
TR40 5 16 16 16 16 145 89 382 0.4 0.1 0.4
TR40 10 16 16 16 16 536 306 402 1.2 0.2 0.5
TR40 15 16 16 16 16 891 401 549 0.9 0.2 0.2
TR40 20 16 14 16 16 736 640 423 0.9 0.2 0.1
TR40 25 16 15 14 16 931 658 383 0.1 0.0 0.0
TR40 30 16 13 16 16 2,004 1,273 975 0.3 0.2 0.2
TR40 35 16 13 14 16 2,598 1,411 777 0.4 0.4 0.4
TR40 40 16 12 11 16 2,718 3,211 633 0.5 0.5 0.5
1. Note that for this set of experiments, all preprocessing and presolving routines of CPLEX as well as its build in additional cuts have been turned off. Average LP gaps are given only over those instances solved by all three models
2. Best values are marked in bold