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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)

From: Pareto optimization in algebraic dynamic programming

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
  1. The computations were performed by using Bellman’s GAP.