Research Article
A Db-Scan Binarization Algorithm Applied to Matrix Covering Problems
Table 6
Comparison between
- and
operators.
| Instance | Best known | - | - | - | - | Best | Avg | Time | Best | Avg | Time | Best | Avg | Time | Best | Avg | Time (s) |
| E.1 | 29 | 29 | 30.8 | 47.4 | 29 | 29.0 | 13.4 | 29 | 29.7 | 37.2 | 29 | 29.0 | 12.1 | E.2 | 30 | 30 | 30.7 | 41.5 | 30 | 30.1 | 13.7 | 30 | 31.3 | 36.5 | 30 | 30.2 | 11.8 | E.3 | 27 | 28 | 30.1 | 39.8 | 27 | 27.5 | 14.1 | 28 | 29.2 | 38.3 | 27 | 27.3 | 12.9 | E.4 | 28 | 29 | 29.8 | 45.7 | 28 | 28.1 | 12.9 | 29 | 29.7 | 37.7 | 28 | 28.0 | 11.5 | E.5 | 28 | 29 | 29.6 | 44.2 | 28 | 28.3 | 13.2 | 29 | 30.1 | 34.1 | 28 | 28.0 | 11.4 |
| F.1 | 14 | 14 | 14.9 | 46.1 | 14 | 14.1 | 12.8 | 14 | 14.9 | 39.5 | 14 | 14.0 | 12.7 | F.2 | 15 | 15 | 15.1 | 49.2 | 15 | 15.4 | 13.5 | 15 | 15.2 | 43.2 | 15 | 15.2 | 13.1 | F.3 | 14 | 14 | 14.6 | 49.3 | 14 | 14.4 | 13.7 | 14 | 14.9 | 47.1 | 14 | 14.1 | 12.6 | F.4 | 14 | 14 | 14.7 | 45.2 | 14 | 14.1 | 13.1 | 14 | 14.8 | 46.3 | 14 | 14.0 | 12.9 | F.5 | 13 | 14 | 14.9 | 41.4 | 13 | 13.4 | 13.4 | 14 | 14.7 | 44.1 | 13 | 13.2 | 13.2 |
| G.1 | 176 | 177 | 178.4 | 286.4 | 176 | 176.8 | 81.3 | 177 | 177.9 | 324.4 | 176 | 177.1 | 73.1 | G.2 | 154 | 157 | 158.3 | 301.3 | 156 | 156.8 | 77.4 | 158 | 159.1 | 351.3 | 156 | 156.6 | 72.6 | G.3 | 166 | 169 | 170.2 | 314.5 | 168 | 168.9 | 79.8 | 170 | 171.4 | 346.7 | 168 | 168.4 | 70.3 | G.4 | 168 | 169 | 170.7 | 322.1 | 169 | 170.1 | 78.1 | 169 | 171.2 | 358.1 | 169 | 169.7 | 68.9 | G.5 | 168 | 169 | 170.5 | 303.1 | 169 | 169.6 | 81.2 | 169 | 169.9 | 354.2 | 168 | 168.2 | 72.1 |
| H.1 | 63 | 64 | 65.1 | 265.2 | 64 | 64.5 | 74.2 | 64 | 65.1 | 286.8 | 64 | 64.8 | 65.3 | H.2 | 63 | 64 | 65.3 | 246.4 | 64 | 64.3 | 73.2 | 64 | 65.7 | 279.4 | 63 | 63.6 | 68.1 | H.3 | 59 | 60 | 61.8 | 298.1 | 60 | 60.4 | 72.1 | 61 | 62.1 | 277.2 | 60 | 60.9 | 69.7 | H.4 | 58 | 59 | 60.3 | 293.7 | 59 | 59.8 | 76.5 | 60 | 60.6 | 298.1 | 59 | 59.2 | 70.3 | H.5 | 55 | 56 | 57.4 | 300.1 | 55 | 55.2 | 74.6 | 56 | 57.2 | 305.2 | 55 | 55.2 | 69.3 |
| Average | 67.1 | 68.0 | 69.16 | 169.03 | 67.6 | 68.04 | 45.11 | 68.2 | 69.23 | 179.27 | 67.5 | 67.84 | 41.2 | Wilcoxon | | 4.6e − 3 | 1.2e − 4 | | | | | 1.05e − 3 | 1.3e − 4 | | | | |
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