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Table 1 Comparison of 2-Phase algorithm and our algorithm in chemical graphs (I)

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
   1 388,192 0.288 741.9E-9 388,192 1,786,467 14.056 6.5E-6 8.7
   2 614 0.021 34.2E-6 614 229 0.134 159.0E-6 4.6
C00062   3 95 0.020 210.5E-6 95 0 0.039 410.5E-6 2.0
C6H14N2O4 12 4 1 0.008 8.0E-3 1 0 0.018 18.0E-3 2.3
   5 1 0.005 5.0E-3 1 0 0.006 6.0E-3 1.2
   6 1 0.006 6.0E-3 1 0 0.006 6.0E-3 1.0
   7 1 0.004 4.0E-3 1 0 0.004 4.0E-3 1.0
   1 1,708 0.007 4.1E-6 1,708 12,626 0.050 3.5E-6 0.9
   2 50 0.004 80.0E-6 50 1,085 0.043 37.9E-6 0.5
C00095   3 0 0.046 0 286 0.046 160.8E-6
C6H12O6 12 4 0 0.006 0 19 0.035 1.8E-3
   5 0 0.004 0 7 0.030 4.3E-3
   6 0 0.004 0 5 0.028 5.6E-3
   7 0 0.004 0 5 0.013 2.6E-3
   1 5,446,987 7.690 1.4E-6 5,446,987 31,395,098 217.681 5.9E-6 4.2
   2 373 0.022 59.0E-6 373 71 0.171 385.1E-6 6.5
C03343   3 187 0.023 123.0E-6 187 25 0.071 334.9E-6 2.7
C16H22O4 15 4 101 0.022 217.8E-6 101 9 0.042 381.8E-6 1.8
   5 51 0.022 431.4E-6 51 6 0.059 1.0E-3 2.4
   6 43 0.009 209.3E-6 43 0 0.036 837.2E-6 4.0
   7 28 0.013 464.3E-6 28 0 0.020 714.3E-6 1.5
   1 2,926,382 2.878 983.5E-9 2,926,382 23,965,432 146.669 5.5E-6 5.5
   2 41,468 1.035 25.0E-6 41,468 213,820 37.792 148.0E-6 5.9
C00645   3 491 0.562 1.1E-3 491 4,482 6.281 1.3E-3 1.1
C8H15NO6 15 4 0 0.523 0 73 4.168 57.1E-3
   5 0 0.374 0 5 2.320 464.0E-3
   6 0 0.135 0 3 0.430 143.3E-3
   7 0 0.121 0 1 0.328 328.0E-3
   1 167,172,180 238.554 1.4E-6 ≥ 1,594,520 ≥ 33,962,677 T. O. 50.7E-6 35.5
   2 210 1.232 5.9E-3 210 641 1.888 2.2E-3 0.4
C00837   3 0 0.853 0 4 1.206 301.5E-3
C8H18N6O4 18 4 0 0.445 0 2 0.523 261.5E-3
   5 0 0.389 0 1 0.596 596.0E-3
   6 0 0.298 0 1 0.367 367.0E-3
   7 0 0.285 0 1 0.395 395.0E-3
   1 62,234,720 321.155 5.2E-6 ≥ 4,812,773 ≥ 40,426,928 T. O. 39.8E-6 7.7
   2 884 0.310 350.7E-6 884 180 1.824 1.7E-3 4.9
C07178   3 22 0.026 1.2E-3 22 4 0.099 3.8E-3 3.2
C21H28N2O5 18 4 1 0.004 4.0E-3 1 0 0.005 5.0E-3 1.3
   5 1 0.004 4.0E-3 1 0 0.005 5.0E-3 1.3
   6 1 0.004 4.0E-3 1 0 0.005 5.0E-3 1.3
   7 1 0.005 5.0E-3 1 0 0.005 5.0E-3 1.0
   1 ≥ 1,208,446,991 T. O. 1.5E-6 ≥ 7,009,856 ≥ 47,008 T. O. 255.1E-6 171.2
   2 27,312,856 965.131 35.3E-6 ≥ 337,989 ≥ 3,593,865 T. O. 458.1E-6 13.0
C00270   3 156,073 391.611 2.5E-3 ≥ 1,546 ≥ 234,187 T. O. 7.6E-3 3.0
C11H19NO9 21 4 0 299.393 ≥ 0 ≥ 165 T. O. 10.9E+0
   5 0 208.268 ≥ 0 ≥ 7 T. O. 257.1E+0
   6 0 19.361 0 2 85.109 42.6E+0
   7 0 9.720 0 2 30.301 15.2E+0
   1 ≥ 664,049,939 T. O. 2.7E-6 ≥ 4,621,297 ≥ 33,216,732 T. O. 47.6E-6 17.5
   2 164,885 34.357 208.4E-6 164,885 1,425 213.810 1.3E-3 6.2
C03690   3 32,995 15.978 484.3E-6 32,995 179 66.612 2.0E-3 4.1
C24H38O4 23 4 3,884 2.265 583.2E-6 3,884 17 5.383 1.4E-3 2.4
   5 1,237 1.490 1.2E-3 1,237 13 3.466 2.8E-3 2.3
   6 559 0.773 1.4E-3 559 0 1.554 2.8E-3 2.0
   7 177 0.445 2.5E-3 177 0 0.617 3.5E-3 1.4