Table 2 Result of algorithms on small graphs
From: Solving the k-dominating set problem on very large-scale networks
Data | \(\text{HEU}_1\) | MILP | \(\text{HEU}_3\) | \(\text{HEU}_4\) | |||||
|---|---|---|---|---|---|---|---|---|---|
Sol | T (s) | Sol | T (s) | Gap | Sol | T (s) | Sol | T (s) | |
\(k = 1\) | |||||||||
s-1 | 21.5 | 0.00 | 17.0 | 147.72 | 0.00 | 19.8 | 0.00 | 17.0 | 0.40 |
s-2 | 29.3 | 0.00 | 19.9 | 403.94 | 0.90 | 23.6 | 0.00 | 19.9 | 0.54 |
s-3 | 77.1 | 0.00 | 53.1 | 403.15 | 0.52 | 57.1 | 0.00 | 49.4 | 12.39 |
s-4 | 90.3 | 0.00 | 64.3 | 400.27 | 0.98 | 56.4 | 0.01 | 53.0 | 12.59 |
s-5 | 98.9 | 0.00 | 72.7 | 400.40 | 0.69 | 61.0 | 0.02 | 58.6 | 12.66 |
\(k = 2\) | |||||||||
s-1 | 13.5 | 0.00 | 10.0 | 52.33 | 0.00 | 12.2 | 0.00 | 10.2 | 0.42 |
s-2 | 10.9 | 0.00 | 5.8 | 36.97 | 0.00 | 6.7 | 0.00 | 5.9 | 0.47 |
s-3 | 20.1 | 0.00 | 12.0 | 400.17 | 0.68 | 13.2 | 0.01 | 11.7 | 2.44 |
s-4 | 15.7 | 0.00 | 4.6 | 403.21 | 0.78 | 4.3 | 0.13 | 4.3 | 7.56 |
s-5 | 6.4 | 0.00 | 4.0 | 406.08 | 0.50 | 4.0 | 0.23 | 4.0 | 11.36 |
\(k = 3\) | |||||||||
s-1 | 9.8 | 0.00 | 7.4 | 8.55 | 0.00 | 8.7 | 0.00 | 7.5 | 0.34 |
s-2 | 3.0 | 0.00 | 2.0 | 0.09 | 0.00 | 2.0 | 0.00 | 2.1 | 0.35 |
s-3 | 5.3 | 0.00 | 2.9 | 2.35 | 0.00 | 3.0 | 0.02 | 2.9 | 0.42 |
s-4 | 1.0 | 0.00 | 1.0 | 0.02 | 0.00 | 1.0 | 0.42 | 1.0 | 0.02 |
s-5 | 1.0 | 0.00 | 1.0 | 0.01 | 0.00 | 1.0 | 0.76 | 1.0 | 0.02 |