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Table 3 The comparison of the lengths of the SCS results obtained by different algorithms on selected DNA and protein sequences.

From: Towards a better solution to the shortest common supersequence problem: the deposition and reduction algorithm

Sequences Length of CS (averaged over 10 instances)
  k n LB ALPHA Ratio MM Ratio DR Ratio
DNA sequences
DNA-1 100 500 686.6 2,000 2.91 1359.7 (18.7) 1.98 1346.4 (19.6) 1.96
DNA-2 500 500 689.5 2,000 2.90 1430.5 (22.1) 2.07 1420.7 (18.1) 2.06
DNA-3 100 1000 1361.0 4,000 2.94 2698.0 (39.9) 1.98 2675.7 (37.2) 1.97
DNA-4 500 1000 1364.4 4,000 2.93 2822.3 (43.4) 2.07 2769.1 (32.7) 2.03
Protein sequences
PROT-1 100 500 800.6 10,000 12.49 5312.7 (81.9) 6.64 4846.3 (73.9) 6.05
PROT-2 500 500 803.5 10,000 12.45 5935.6 (61.8) 7.39 5548.6 (54.3) 6.91
PROT-3 1000 500 809.8 10,000 12.35 6082.4 (44.9) 7.51 5734.0 (43.9) 7.08
  1. The average and standard deviation (in parenthesis) are given. The estimated performance ratios are also given for each algorithm.