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Table 1 Comparison of previous method and our method

From: Enumerating tree-like chemical graphs with given upper and lower bounds on path frequencies

Entry Formula      SimEnum RepEnum
  n K w f v time (s) nodes solutions time (s) nodes solutions solved
   1 1 36 1037.04 177,074,686 414,890 163.32 44,340,488 414,890 729
   2 1 318 2.97 392,246 44 T.O. 2,381,360,000 N.F. 65,909,572
   3 1 334 1.22 145,213 2 T.O. 3,293,260,000 N.F. 96,860,588
C00062 26 4 1 353 0.33 34,539 1 T.O. 2,780,050,000 N.F. 81,766,176
C6H14N2O4   5 1 371 0.24 20,361 1 T.O. 1,561,230,000 N.F. 45,918,529
   6 1 385 0.25 15,166 1 T.O. 569,590,000 N.F. 16,752,647
   7 1 396 0.18 14,547 1 T.O. 79,870,000 N.F. 2,349,117
   1 1 36 T.O. 377,260,000 N.F. T.O. 413,000,000 N.F. 460
   2 1 318 7.24 845,760 25 T.O. 1,442,760,000 N.F. 70,175,902
   3 1 331 2.81 307,151 7 T.O. 3,316,970,000 N.F. 195,115,882
C03343 37 4 1 347 1.03 99,945 1 T.O. 2,494,780,000 N.F. 146,751,764
C16H22O4   5 1 364 0.98 87,600 1 T.O. 1,050,480,000 N.F. 61,792,941
   6 1 382 0.76 60,194 1 T.O. 315,820,000 N.F. 18,577,647
   7 1 399 0.57 42,538 1 T.O. 41,450,000 N.F. 2,438,235
   1 1 38 T.O. 157,320,000 N.F. T.O. 200,490,000 N.F. 1,388
   2 1 326 37.59 1,940,295 238 T.O. 2,911,390,000 N.F. 66,167,954
   3 1 348 1.71 60,792 3 T.O. 2,673,940,000 N.F. 60,771,363
C07178 46 4 1 371 0.35 14,248 1 T.O. 1,925,490,000 N.F. 43,761,136
C21H28N2O5   5 1 392 0.27 10,866 1 T.O. 743,940,000 N.F. 16,907,727
   6 1 3110 0.27 10,680 1 T.O. 93,880,000 N.F. 2,133,636
   7 1 3125 0.24 9,276 1 T.O. 19,270,000 N.F. 437,954
   1 1 35 T.O. 382,470,000 N.F. T.O. 552,290,000 N.F. 61
   2 1 316 T.O. 211,800,000 N.F. T.O. 530,930,000 N.F. 10,451,912
   3 1 327 1395.13 144,244,042 206 T.O. 3,314,260,000 N.F. 194,956,470
C03690 61 4 1 341 121.36 11,332,363 4 T.O. 2,392,530,000 N.F. 140,737,058
C24H38O4   5 1 357 83.70 6,978,557 2 T.O. 958,650,000 N.F. 56,391,176
   6 1 375 40.11 2,923,819 1 T.O. 298,600,000 N.F. 17,564,705
   7 1 392 16.50 1,096,128 1 T.O. 38,670,000 N.F. 2,274,705
  1. Comparison of SimEnum and RepEnum for the problem ETULF.
  2. Note:
  3. (1) C00062, C03343, C07178, and C03630 are the chemical compounds in the KEGG LIGAND database, respectively;
  4. (2) n is the number of vertices in an instance preprocessed by replacing each benzene ring with a new atom having six valences;
  5. (3) K is the level of given feature vectors;
  6. (4) w is the width for constructing upper and lower feature vectors;
  7. (5) f v is the number of feature vectors in a given set;
  8. (6) “time (s)” is the CPU time in seconds;
  9. (7) T.O. means “time over” (the time limit is set to be 1,800 seconds);
  10. (8) “nodes” is (the sum of) the number of nodes of family trees that are traversed;
  11. (9) “solutions” is the number of all possible solutions;
  12. (10) “solved” is the number of feature vectors which the algorithm RepEnum solved in the time limit; and (11) N.F. means “not found.”