Table 3 Runtimes and memory requirements for MFE(k), MEA(k) (where k is the empirical Pareto front size for a given input), and their Pareto product \(({MFE}\,\, {*}_{\text {Par}}\,\,{MEA})\), accumulated over 331 sequences (left) and for the longest sequence (\(n = 356, k = 38\), right)
| Algebra | Time (min) | Memory (GB) | Time (min) | Memory (GB) |
|---|---|---|---|---|
| MFE(k) alone | 71 | 163.68 | 5 | 1.16 |
| MEA(k) alone | 61 | 153.51 | 5 | 1.05 |
| MFE(k) + MEA(k) | 132 (+) | 163.68 (max) | 10 | 1.16 (max) |
| \(({MFE} {*}_{\text {Par}}{MEA})\) | ||||
| \(~~~{\mathbf{pf}} _\text {nosort}\) | 8 | 197.28 | 0.22 | 1.28 |
| \(~~~{\mathbf{pf}} _\text {smooth}\) | 9.5 | 192.79 | 0.5 | 1.28 |
| \(~~~{\mathbf{pf}} _\text {sort}\) | 18 | 271.21 | 1 | 1.28 |
| \(~~~{\mathbf{pf}} _\text {isort}\) | 32 | 250.21 | 3 | 2.11 |