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Table 2 Comparison of varying width w in chemical graphs (I)

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

Entry

   

2-Phase Algorithm

Our Algorithm

 

Formula

n

w

K

Tree

Time

Time/graph

Tree

Cycle

Time

Time/graph

Ratio

  

1

3

95

0.020

210.5E-6

95

0

0.039

410.5E-6

2.0

  

2

3

862

0.020

23.2E-6

862

100

0.130

135.1E-6

5.8

C00062

 

3

3

2,531

0.030

11.8E-6

2,531

894

0.213

62.2E-6

5.3

C6H14N2O4

12

4

3

3,611

0.044

12.2E-6

3,611

2,737

0.254

40.0E-6

3.3

  

5

3

4,438

0.044

9.9E-6

4,438

5,454

0.265

26.8E-6

2.7

  

50

3

5,138

0.045

8.8E-6

5,138

12,044

0.388

22.6E-6

2.6

  

1

3

0

0.005

–

0

286

0.046

160.8E-6

–

  

2

3

40

0.065

1.6E-3

40

1,569

0.065

40.4E-6

0.0

C00095

 

3

3

280

0.009

32.1E-6

280

4,899

0.089

17.2E-6

0.5

C6H12O6

12

4

3

855

0.010

11.7E-6

855

8,273

0.148

16.2E-6

1.4

  

5

3

1,502

0.011

7.3E-6

1,502

12,085

0.177

13.0E-6

1.8

  

50

3

4,608

0.012

2.6E-6

4,608

23,686

0.186

6.6E-6

2.5

  

1

3

187

0.023

123.0E-6

187

25

0.071

334.9E-6

2.7

  

2

3

2,077

0.091

43.8E-6

2,077

1,251

0.880

264.4E-6

6.0

C03343

 

3

3

5,345

0.201

37.6E-6

5,345

5,746

3.134

282.6E-6

7.5

C16H22O4

15

4

3

10,391

0.346

33.3E-6

10,391

16,912

4.041

148.0E-6

4.4

  

5

3

14,531

0.482

33.2E-6

14,531

33,064

5.887

123.7E-6

3.7

  

50

3

19,819

0.655

33.0E-6

19,819

94,725

7.833

68.4E-6

2.1

  

1

3

491

0.562

1.1E-3

491

4,482

6.281

1.3E-3

1.1

  

2

3

7,846

1.122

143.0E-6

7,846

76,261

17.199

204.5E-6

1.4

C00645

 

3

3

151,227

2.420

16.0E-6

151,227

716,216

39.476

45.5E-6

2.8

C8H15NO6

15

4

3

216,507

2.946

13.6E-6

216,507

1,270,462

33.842

22.8E-6

1.7

  

5

3

272,898

3.405

12.5E-6

272,898

1,757,010

40.323

19.9E-6

1.6

  

50

3

355,958

3.985

11.2E-6

355,958

2,625,154

43.002

14.4E-6

1.3

  

1

3

0

0.853

–

0

4

1.206

301.5E-3

–

  

2

3

389

1.569

4.0E-3

389

660

2.496

2.4E-3

0.6

C00837

 

3

3

2,510

1.999

796.4E-6

2,510

3,173

3.367

592.5E-6

0.7

C8H18N6O4

18

4

3

8,544

2.314

270.8E-6

8,544

12,834

3.994

186.8E-6

0.7

  

5

3

13,796

2.465

178.7E-6

13,796

27,186

4.841

118.1E-6

0.7

  

50

3

24,313

2.683

110.4E-6

24,313

94,089

5.540

46.8E-6

0.4

  

1

3

22

0.026

1.2E-3

22

4

0.099

3.8E-3

3.2

  

2

3

386

0.058

150.3E-6

386

261

0.426

658.4E-6

4.4

C07178

 

3

3

2,376

0.089

37.5E-6

2,376

1,288

0.735

200.6E-6

5.4

C21H28N2O5

18

4

3

4,092

0.102

24.9E-6

4,092

2,240

0.863

136.3E-6

5.5

  

5

3

4,629

0.109

23.5E-6

4,629

2,385

1.284

183.1E-6

7.8

  

50

3

5,103

0.115

22.5E-6

5,103

2,603

0.980

127.2E-6

5.6

  

1

3

156,073

391.611

2.5E-3

≥ 1,546

≥ 234,187

T. O.

7.6E-3

3.0

  

2

3

12,515,364

1331.770

106.4E-6

≥ 93,244

≥ 1,107,707

T. O.

1.5E-3

14.1

C00270

 

3

3

≥ 88,182,895

T. O.

20.4E-6

≥ 4,350,635

≥ 1,135,547

T. O.

328.3E-6

16.1

C11H19NO9

21

4

3

≥ 134,281,382

T. O.

13.4E-6

≥ 5,230,515

≥ 2,086,287

T. O.

246.0E-6

18.4

  

5

3

≥ 169,965,948

T. O.

10.6E-6

≥ 5,213,010

≥ 2,383,696

T. O.

237.1E-6

22.4

  

50

3

≥ 254,637,067

T. O.

7.1E-6

≥ 7,025,893

≥ 12,785,700

T. O.

90.9E-6

12.9

  

1

3

32,995

15.978

484.3E-6

32,995

179

66.612

2.0E-3

4.1

  

2

3

2,472,133

149.048

60.3E-6

≥ 1,763,123

≥ 702,493

T. O.

730.0E-6

12.1

C03690

 

3

3

13,120,833

509.010

38.8E-6

≥ 2,416,279

≥ 2,028,470

T. O.

405.0E-6

10.4

C24H38O4

23

4

3

43,379,162

1289.269

29.7E-6

≥ 1,815,035

≥ 4,297,658

T. O.

294.5E-6

9.9

  

5

3

≥ 80,447,027

T. O.

22.4E-6

≥ 2,828,014

≥ 10,431,681

T. O.

135.7E-6

6.1

  

50

3

≥ 111,576,848

T. O.

16.1E-6

≥ 3,580,958

≥ 55,327,406

T. O.

30.6E-6

1.9

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Journal of Cheminformatics

ISSN: 1758-2946

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