Research Article
An Improved Exact Algorithm for Least-Squares Unidimensional Scaling
Table 1
Performance on random problem instances.
| Inst.
| Objective function value
| B&B | BB3 | | Number of nodes | Time | Number of nodes | Time |
| | p20 | 9053452 (179755.4; 0.284) | 1264871 | 4.4 | 1526725 | 5.6 | | p21 | 9887394 (187927.7; 0.285) | 3304678 | 10.6 | 4169099 | 14.5 | | p22 | 12548324 (224540.6; 0.282) | 6210311 | 20.5 | 8017112 | 29.0 | | p23 | 14632006 (239619.8; 0.274) | 12979353 | 45.0 | 16624663 | 1:06.7 | | p24 | 16211210 (281585.9; 0.294) | 31820463 | 1:53.3 | 42435561 | 2:55.5 | | p25 | 15877026 (312670.0; 0.330) | 103208158 | 6:44.6 | 137525505 | 9:52.4 | | p26 | 20837730 (347147.8; 0.302) | 200528002 | 13:35.4 | 267603807 | 20:43.6 | | p27 | 21464870 (358595.8; 0.311) | 287794935 | 20:37.7 | 392405143 | 32:36.5 | | p28 | 23938264 (396136.0; 0.317) | 581602877 | 44:09.3 | 812649051 | 1:13:05.4 | | p29 | 28613820 (453778.6; 0.315) | 2047228373 | 2:50:57.2 | 3044704554 | 4:38:57.0 | | p30 | 30359134 (464556.9; 0.315) | 3555327537 | 5:09:09.9 | 5216804247 | 8:55:04.6 |
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