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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.