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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.