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Table 3 Comparison of 2-Phase algorithm and our algorithm in chemical graphs (II)

From: Efficient enumeration of monocyclic chemical graphs with given path frequencies

Entry

  

2-Phase Algorithm

Our Algorithm

 

Formula

n

K

Tree

Time

Time/graph

Tree

Cycle

Time

Time/graph

Ratio

  

1

2,609

0.006

2.3E-6

2,609

11,263

0.036

2.6E-6

1.1

  

2

193

0.007

36.3E-6

193

165

0.015

41.9E-6

1.2

D08040

 

3

14

0.009

642.9E-6

14

5

0.014

736.8E-6

1.1

C5H9N3

8

4

9

0.005

555.6E-6

9

2

0.006

545.5E-6

1.0

  

5

4

0.004

1.0E-3

4

1

0.005

1.0E-3

1.0

  

6

4

0.004

1.0E-3

4

1

0.005

1.0E-3

1.0

  

7

1

0.005

1.3E-3

4

1

0.006

1.2E-3

0.9

  

1

17,470

0.127

7.2E-6

17,470

264,326

1.446

5.1E-6

0.7

  

2

1,183

0.023

19.4E-6

1,183

16,233

0.294

17.9E-6

0.9

D00332

 

3

30

0.017

566.7E-6

30

1,318

0.170

126.1E-6

0.2

C9H17NO2

12

4

0

0.025

–

0

292

0.112

383.6E-6

–

  

5

0

0.034

–

0

41

0.090

2.2E-3

–

  

6

0

0.021

–

0

12

0.050

4.1E-3

–

  

7

0

0.016

–

0

8

0.037

4.6E-3

–

  

1

54,072,616

200.647

3.7E-6

≥11,645,178

≥110,673,601

T.O.

14.7E-6

4.0

  

2

68,253

5.458

80.0E-6

68,253

321,853

130.500

334.2E-6

4.2

D00555

 

3

4,590

4.115

896.5E-6

4,590

6,511

70.821

6.4E-3

7.1

C11H18N2O3

16

4

91

2.702

29.7E-3

91

278

28.632

77.5E-3

2.6

  

5

0

1.438

–

0

38

15.129

397.3E-3

–

  

6

0

0.694

–

0

5

6.882

1.4E+0

–

  

7

0

0.211

–

0

1

0.663

663.0E-3

–

  

1

≥10,280

T.O.

175.1E-3

≥1,432

≥883,812

T.O.

2.0E-3

0.0

  

2

≥19,587,838

T.O.

91.9E-6

≥0

≥0

T.O.

–

–

D00079

 

3

≥1,134,806

T.O.

1.6E-3

≥21,048

≥0

T.O.

85.5E-3

53.4

C20H32O5

25

4

≥17,852

T.O.

100.8E-3

≥0

≥0

T.O.

–

–

  

5

≥23

T.O.

78.3E+0

≥0

≥0

T.O.

–

–

  

6

≥0

T.O.

–

≥0

≥0

T.O.

–

–

  

7

≥0

T.O.

–

≥0

≥0

T.O.

–

–

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Journal of Cheminformatics

ISSN: 1758-2946

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