Research Article
A Db-Scan Binarization Algorithm Applied to Matrix Covering Problems
Table 3
Comparison between
- and
operators.
| Instance | Best known | - | -0.25- | -0.5- | Best | Avg | Time (s) | Best | Avg | Time (s) | Best | Avg | Time (s) |
| E.1 | 29 | 29 | 29.0 | 12.1 | 29 | 30.4 | 7.7 | 29 | 30.7 | 8.2 | E.2 | 30 | 30 | 30.2 | 11.8 | 31 | 32.6 | 8.1 | 30 | 32.4 | 7.8 | E.3 | 27 | 27 | 27.3 | 12.9 | 28 | 29.4 | 6.6 | 28 | 29.8 | 8.1 | E.4 | 28 | 28 | 28.0 | 11.5 | 29 | 30.3 | 6.5 | 28 | 30.7 | 8.3 | E.5 | 28 | 28 | 28.0 | 11.4 | 29 | 29.8 | 6.7 | 28 | 30.1 | 8.2 |
| F.1 | 14 | 14 | 14.0 | 12.7 | 15 | 16.1 | 9.1 | 15 | 16.9 | 14.1 | F.2 | 15 | 15 | 15.2 | 13.1 | 16 | 17.8 | 8.7 | 16 | 18.1 | 15.3 | F.3 | 14 | 14 | 14.1 | 12.6 | 15 | 15.4 | 9.3 | 15 | 15.5 | 14.8 | F.4 | 14 | 14 | 14.0 | 12.9 | 15 | 16.2 | 9.4 | 15 | 16.2 | 14.9 | F.5 | 13 | 13 | 13.2 | 13.2 | 14 | 15.7 | 8.9 | 14 | 15.9 | 14.1 |
| G.1 | 176 | 176 | 177.1 | 73.1 | 183 | 187.4 | 54.6 | 184 | 189.1 | 60.3 | G.2 | 154 | 156 | 156.6 | 72.6 | 162 | 167.1 | 57.3 | 161 | 166.3 | 61.2 | G.3 | 166 | 168 | 168.4 | 70.3 | 174 | 179.4 | 58.6 | 173 | 178.4 | 59.7 | G.4 | 168 | 169 | 169.7 | 68.9 | 173 | 177.2 | 56.6 | 174 | 178.2 | 60.5 | G.5 | 168 | 168 | 168.2 | 72.1 | 172 | 176.7 | 54.1 | 171 | 177.8 | 58.1 |
| H.1 | 63 | 64 | 64.8 | 65.3 | 68 | 72.3 | 52.7 | 68 | 73.1 | 54.9 | H.2 | 63 | 63 | 63.6 | 68.1 | 69 | 73.1 | 55.3 | 68 | 73.5 | 53.1 | H.3 | 59 | 60 | 60.9 | 69.7 | 64 | 68.4 | 57.2 | 64 | 67.9 | 58.9 | H.4 | 58 | 59 | 59.2 | 70.3 | 63 | 66.3 | 56.6 | 62 | 67.1 | 60.4 | H.5 | 55 | 55 | 55.2 | 69.3 | 61 | 64.2 | 55.3 | 60 | 64.9 | 59.1 |
| Average | 67.1 | 67.5 | 67.84 | 41.2 | 70.5 | 73.29 | 31.97 | 70.1 | 73.63 | 35.0 | Wilcoxon | | | | | 1.03e−4 | 8.84e−5 | | 5.20e−4 | 8.85e−5 | |
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