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 $(MFE{\ast }_{\text{Par}}MEA)$, 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)
$(MFE{\ast }_{\text{Par}}MEA)$
${\mathbf{pf}}_{\text{nosort}}$	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

The computations were performed by using Bellman’s GAP.