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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