Algorithm 3: Your own creation

Do whatever you like to try and beat the performance of algorithms 1 and 2. If you discover a smaller dominating set than the minimum known for one of the open problems, be sure to let me know.

Student Results

These are best viewed on a wide screen with a small font size.


C80 fullerenes:
 
  #     n :  k 1    k 2    k 3    k 4    k 5    k 6    k 7    k 8    k 9    k10    k11    k12    k13    k14    k15    k16    k17    k18    k19    k20  
  1    80 :   20     22     29     20-    22     20-    22     20-    26     20-    25     22     22     30     20-    22     22     34+    24     20- 
  2    80 :   20     22     31     20-    23     20-    23     20-    25     20-    25     22     22     32     20-    23     25     36+   ---     20- 
  3    80 :   20     22     32     20-    22     20-    22     20-    25     20-    25     23     22     29     20-    22     25     34+   ---     20- 
  4    80 :   20     22     31     20-    22     20-    22     20-    24     20-    25     22     22     29     20-    22     25     34+   ---     20- 
  5    80 :   20     23     31     20-    22     20-    22     20-    24     20-    25     22     21     25     20-    22     24     35+   ---     20- 
  6    80 :   20     22     31     20-    22     20-    23     20-    25     20-    25     22     22     27     20-    22     26     33+   ---     20- 
  7    80 :   20     22     30     20-    22     20-    22     20-    24     20-    25     22     22     24     20-    22     25     34+   ---     20- 
  8    80 :   20     22     31     20-    22     20-    22     20-    25     35+    25     22     22     27     20-    22     25     34    ---     20- 
  9    80 :   20     22     29     20-    23     20-    23     20-    25     40+    23     22     22     29     20-    22     24     33    ---     20- 
 10    80 :   20     22     31     20-    23     20-    22     20-    26     36+    25     22     22     28     20-    22     26     34    ---     20- 
 11    80 :   20     22     29     20-    22     20-    20-    20-    25     20-    25     22     21     29     20-    22     24     34+   ---     20- 
 12    80 :   21     22     26     21-    23     22     22     21-    26     21-    25     23     22     27     21-    22     24     36+   ---     21- 
 13    80 :   21     22     27     21-    23     21-    22     21-    27     21-    25     23     22    ---     21-    23     25     36+   ---     21- 
 14    80 :   21     22     29     21-    23     21-    23     21-    25     21-    24     22     22    ---     22     22     24     35+   ---     21- 
 15    80 :   21     22     27     21-    23     21-    23     21-    26     21-    24     23     22    ---     21-    22     24     35+   ---     21- 
 16    80 :   21     22     30     21-    23     21-    22     21-    25     21-    23     22     22    ---     22     22     26     35+   ---     21- 
 17    80 :   21     22     30     21-    23     21-    23     21-    25     21-    24     22     21-   ---     22     22     25     35+   ---     21- 
 18    80 :   21     22     31     21-    23     21-    23     21-    25     21-    23     22     22    ---     22     22     24     35+   ---     21- 
 19    80 :   21     22     28     21-    23     21-    24     21-    26     21-    23     22     22    ---     21-    22     25     35+   ---     21- 
 20    80 :   21     22     29     21-    23     21-    23     21-    26     21-    23     22     22    ---     21-    22     25     35+   ---     21- 
 21    80 :   21     23     30     21-    23     21-    23     21-    27     21-    24     23     22    ---     21-    23     26     35+   ---     21- 
 22    80 :   21     22     29     21-    23     21-    22     21-    26     21-    22     22     22    ---     22     22     25     35+   ---     21- 
 23    80 :   22     22-    28     22-    23     22-    22-    22-    24     22-    23     22-    22-   ---     22-    22-    26     35+   ---     22- 
 24    80 :   22     23     26     22-    24     22-    24     22-    25     22-    24     22-    22-   ---     22-    22-    25     37+   ---     22- 
 25    80 :   22     22-    26     22-    23     22-    22-    22-    25     22-    24     22-    22-   ---     22-    23     25     37+   ---     22- 
 26    80 :   22     23     27     22-    23     22-    22-    22-    25     22-    24     23     23    ---     22-    22-    25     37+   ---     22- 
 27    80 :   22     22-    27     22-    22-    22-    22-    22-    26     22-    24     22-    22-   ---     22-    22-    25     33+   ---     22- 
 28    80 :   22     23     27     22-    22-    22-    22-    22-    27     22-    24     22-    22-   ---     22-    22-    26     33+   ---     22- 
 29    80 :   22     23     25     22-    22-    22-    22-    22-    25     22-    24     23     22-   ---     22-    22-    26     34+   ---     22- 
 30    80 :   22     22-    25     22-    22-    22-    22-    22-    25     22-    24     23     22-   ---     22-    23     24     34+   ---     22- 
 31    80 :   22     22-    30     22-    23     22-    23     22-    25     22-    25     22-    22-   ---     22-    23     25     36+   ---     22- 
 32    80 :   22     23     28     22-    23     22-    23     22-    24     22-    25     22-    22-   ---     22-    22-    26     36+   ---     22- 
 33    80 :   22     23     30     22-    23     22-    22-    22-    26     22-    25     22-    22-   ---     22-    22-    26     36+   ---     22- 

Rank  1: Student  4 with score   0
Rank  1: Student  8 with score   0
Rank  1: Student 20 with score   0
Rank  4: Student  6 with score   1
Rank  5: Student 15 with score   5
Rank  6: Student 13 with score  31
Rank  7: Student 16 with score  39
Rank  8: Student  2 with score  41
Rank  8: Student 12 with score  41
=====================================
Rank 10: Student  7 with score  46
Rank 11: Student 10 with score  51
Rank 12: Student  5 with score  55
Rank 13: Student 11 with score 106
Rank 14: Student 17 with score 130
Rank 15: Student  9 with score 142
Rank 16: Student  3 with score 257
Rank 17: Student 18 with score 457
Rank 18: Student 14 with score 1775
Rank 19: Student 19 with score 2564

 
Football distance 1:
 
  #     n :  k 1    k 2    k 3    k 4    k 5    k 6    k 7    k 8    k 9    k10    k11    k12    k13    k14    k15    k16    k17    k18    k19    k20  
  1     9 :    3      3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3- 
  2    27 :    5      5-     6      5-     5-     6      5-     5-     5-     5-     5-     5-     5-     5-     5-     5-     5-     7+     5-     5- 
  3    81 :    9      9-    18      9-    27+     9-     9-    27+    15     20     14      9-     9-    15      9-     9-    14     21     13      9- 
  4   243 :   27     35     56     65     81+    36     27-    81+    39     78     41     36     31     38     39     35     41     61     41     33  
  5   729 :   73    105    152    235    243     99     93    243    107    241    112    105     92-   105    110    107    110    730+   117     93  
  6  2187 :  186    302    473    725    729    292    245-   729    286   1667    320    303   2187+  2187+   ---    300    311    ---    ---    247  

Rank  1: Student  7 with score  79
Rank  2: Student 20 with score  87
Rank  3: Student  6 with score 142
Rank  4: Student  9 with score 152
Rank  5: Student  2 with score 156
Rank  5: Student 16 with score 156
=====================================
Rank  7: Student 12 with score 158
Rank  8: Student 17 with score 181
Rank  9: Student 11 with score 192
Rank 10: Student  3 with score 405
Rank 11: Student  4 with score 739
Rank 12: Student  5 with score 785
Rank 12: Student  8 with score 785
Rank 14: Student 10 with score 1711
Rank 15: Student 13 with score 2024
Rank 16: Student 14 with score 2050
Rank 17: Student 15 with score 2236
Rank 18: Student 19 with score 2249
Rank 19: Student 18 with score 2892

 
Football distance 2:
 
  #     n :  k 1    k 2    k 3    k 4    k 5    k 6    k 7    k 8    k 9    k10    k11    k12    k13    k14    k15    k16    k17    k18    k19    k20  
  1    27 :    3      3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3- 
  2    81 :    3      3-     6      3-     5      3-     3-     3-     5      3-     3-     3-     3-     5      3-     3-     4      9+     3-     3- 
  3   243 :    8      9     16     12     27+    11      9     27+    12     21     10      9      9     12      9      9     11      9      9      8- 
  4   729 :   17     25     44     72     81     28     22     81     30    124     25     24     21-    31     30     26     28    730+    25     21- 
  5  2187 :   34     65    133    237    243     72     52-   243     67   1757+    71     64     56     69    ---     65     66    ---     70     53  

Rank  1: Student 20 with score  23
Rank  2: Student  7 with score  24
Rank  3: Student 13 with score  27
Rank  4: Student 12 with score  38
Rank  5: Student  2 with score  40
=====================================
Rank  6: Student 16 with score  41
Rank  7: Student 19 with score  45
Rank  8: Student 11 with score  47
Rank  8: Student 17 with score  47
Rank 10: Student  6 with score  52
Rank 10: Student  9 with score  52
Rank 12: Student 14 with score  55
Rank 13: Student  3 with score 137
Rank 14: Student  4 with score 262
Rank 15: Student  8 with score 292
Rank 16: Student  5 with score 294
Rank 17: Student 10 with score 1843
Rank 18: Student 15 with score 2201
Rank 19: Student 18 with score 2907

 
Football distance 3:
 
  #     n :  k 1    k 2    k 3    k 4    k 5    k 6    k 7    k 8    k 9    k10    k11    k12    k13    k14    k15    k16    k17    k18    k19    k20  
  1    81 :    3      3-     3-     3-     3-     3-     3-   ---      3-     3-     3-     3-   ---      3-     3-     3-     3-     3-     3-     3- 
  2   243 :    3      3-     7+     3-     6      3-     3-   ---      5      3-     3-     3-   ---      5      3-     3-     3-     3-     3-     3- 
  3   729 :    6      7     12     13     27      6-     6-   ---     10    244      7      8    ---     14     10      6-     9    730+     7      6- 
  4  2187 :   12     19     29     78     81     31     16    ---     22    ---     19     18    ---   2187+   ---     18     20    ---     19     15- 

Rank  1: Student 20 with score   3
Rank  2: Student  7 with score   4
Rank  3: Student 16 with score   6
Rank  4: Student  2 with score   8
Rank  4: Student 11 with score   8
Rank  4: Student 12 with score   8
Rank  4: Student 19 with score   8
=====================================
Rank  8: Student 17 with score  11
Rank  9: Student  9 with score  16
Rank 10: Student  6 with score  19
Rank 11: Student  3 with score  27
Rank 12: Student  4 with score  73
Rank 13: Student  5 with score  93
Rank 14: Student 14 with score 2185
Rank 15: Student 15 with score 2191
Rank 16: Student 10 with score 2425
Rank 17: Student 18 with score 2911
Rank 18: Student  8 with score 3240
Rank 18: Student 13 with score 3240

 
Hypercube distance 1:
 
  #     n :  k 1    k 2    k 3    k 4    k 5    k 6    k 7    k 8    k 9    k10    k11    k12    k13    k14    k15    k16    k17    k18    k19    k20  
  1     8 :    2      2-     4+     2-     2-     2-     2-     2-     2-     2-     2-     2-     2-     2-     2-     2-     2-     4+     2-     2- 
  2    16 :    4      4-     5      4-     4-     5      4-     4-     4-     4-     4-     4-     4-     4-     4-     4-     4-     8+     4-     4- 
  3    32 :    7      7     10      7     10      8      7      7      8      7      7      6-     7      7      7      7      7     16+     7      7  
  4    64 :   12     12-    19     12-    22     16     13     16     15     16     12-    12-    12-    14     12-    12-    14     32+    12-    12- 
  5   128 :   16     16-    44     34     48     16-    16-    38     25     50     26     22     17     28     23     20     27     64+    27     16- 
  6   256 :   32     45    102     99    128+    41     32-   102     47    118     50     44     38     48     46     45     48    128+    49     39  
  7   512 :   62     88    184    233    256+    82     71-   232     89    249     94     89     78     95     86     87     95    256+    92     75  
  8  1024 :  120    169    372    495    512    162    143-   490    168    509    180    171    151    171    174    171    177   1025+   183    147  
  9  2048 :  192    335    764   1012   1024    308    270-  1006    307   1511    339    325   2048+   331    ---    330    337    ---    ---    277  

Rank  1: Student  7 with score 111
Rank  2: Student 20 with score 132
Rank  3: Student  6 with score 193
Rank  4: Student  9 with score 218
Rank  5: Student 12 with score 228
Rank  6: Student  2 with score 231
Rank  6: Student 16 with score 231
=====================================
Rank  8: Student 14 with score 253
Rank  9: Student 17 with score 264
Rank 10: Student 11 with score 267
Rank 11: Student  3 with score 1057
Rank 12: Student  8 with score 1450
Rank 13: Student  4 with score 1451
Rank 14: Student  5 with score 1559
Rank 15: Student 13 with score 1910
Rank 16: Student 10 with score 2019
Rank 17: Student 15 with score 2147
Rank 18: Student 19 with score 2169
Rank 19: Student 18 with score 3326

 
Hypercube distance 2:
 
  #     n :  k 1    k 2    k 3    k 4    k 5    k 6    k 7    k 8    k 9    k10    k11    k12    k13    k14    k15    k16    k17    k18    k19    k20  
  1    32 :    2      2-     4+     2-     2-     2-     2-     2-     4+     2-     2-     2-     2-     4+     2-     2-     2-     4+     2-     2- 
  2    64 :    4      4-     8+     4-     4-     6      4-     4-     5      4-     4-     4-     4-     5      4-     4-     4-     8+     4-     4- 
  3   128 :    7      7-    17      7-    19+     8      7-    16      7-     8      8      7-     7-    11      7-     7-     8     16      7-     7- 
  4   256 :   12     13     35     18     46+    16     12-    39     14     36     15     13     12-    18     14     12-    15     16     14     12- 
  5   512 :   16     24     74     75    116+    27     22-   102     26    116+    29     24     22-    28     28     24     26     32     26     22- 
  6  1024 :   30     45    141    216    256     49     37-   232     49    448     48     46     38     51     44     46     47   1025+    45     37- 
  7  2048 :   44     81    284    493    512     84     64-   490     84   1589     87     84     70   2048+   ---     82     84    ---     86     65  

Rank  1: Student  7 with score  33
Rank  2: Student 20 with score  34
Rank  3: Student 13 with score  40
Rank  4: Student  2 with score  61
=====================================
Rank  5: Student 16 with score  62
Rank  6: Student 12 with score  65
Rank  7: Student 19 with score  69
Rank  8: Student 17 with score  71
Rank  9: Student  9 with score  74
Rank 10: Student  6 with score  77
Rank 11: Student 11 with score  78
Rank 12: Student  3 with score 448
Rank 13: Student  4 with score 700
Rank 14: Student  8 with score 770
Rank 15: Student  5 with score 840
Rank 16: Student 14 with score 2050
Rank 17: Student 15 with score 2076
Rank 18: Student 10 with score 2088
Rank 19: Student 18 with score 3078

 
Hypercube distance 3:
 
  #     n :  k 1    k 2    k 3    k 4    k 5    k 6    k 7    k 8    k 9    k10    k11    k12    k13    k14    k15    k16    k17    k18    k19    k20  
  1   128 :    2      2-     6      2-     2-     2-     2-     2-     4      2-     2-     2-   ---      4      2-     2-     2-     8+     2-     2- 
  2   256 :    4      4-     7      4-    18+     7      4-    16      4-     4-     4-     4-   ---      8      4-     4-     4-    16      4-     4- 
  3   512 :    7      8     16      9     40      9      7-    40     10     42+     8      8    ---     11      9      8      9     16      8      7- 
  4  1024 :   12     15     32     91    105     18     13    105     16    562     19     15    ---     19     21     15     17   1025+    16     12- 
  5  2048 :   16     26     56    246    242     40     22-   237     28   1681     27     26    ---   2048+   ---     27     29    ---     27     22- 

Rank  1: Student 20 with score   6
Rank  2: Student  7 with score   7
Rank  3: Student  2 with score  14
Rank  3: Student 12 with score  14
=====================================
Rank  5: Student 16 with score  15
Rank  6: Student 19 with score  16
Rank  7: Student 11 with score  19
Rank  8: Student 17 with score  20
Rank  9: Student  9 with score  21
Rank 10: Student  6 with score  35
Rank 11: Student  3 with score  76
Rank 12: Student  4 with score 311
Rank 13: Student  8 with score 359
Rank 14: Student  5 with score 366
Rank 15: Student 14 with score 2049
Rank 16: Student 15 with score 2059
Rank 17: Student 10 with score 2250
Rank 18: Student 18 with score 3088
Rank 19: Student 13 with score 3968

 
Kneser Graphs:
 
  #     n :  k 1    k 2    k 3    k 4    k 5    k 6    k 7    k 8    k 9    k10    k11    k12    k13    k14    k15    k16    k17    k18    k19    k20  
  1    35 :    7      7-    10+     7-     7-     7-     7-     7-    10+     7-     7-     7-     7-    10+     7-     7-     7-    10+     7-     7- 
  2    56 :    7      7-    14      7-    16+     9      7-    12     10      7-     7-     7-     7-    10      8      7-     9     10      7-     7- 
  3    84 :    7      7-    10      7-    19+     7-     7-    16      9      7-     7-     7-     7-    10      7-     7-     8     10      7-     7- 
  4   120 :    6      6-     9      6-    22+     7      6-    22+     6-     6-     6-     6-     6-    10      6-     6-     7     10      6-     6- 
  5   165 :    5      5-     8      5-    25+     7      5-    25+     9      5-     5-     5-     5-     9      5-     5-     6     10      5-     5- 
  6   220 :    4      4-     7      4-    28+     7      4-    28+     7      5      4-     4-     4-     9      4-     4-     5     10      4-     4- 
  7   286 :    4      4-     7      4-    31+     7      4-    31+     6      5      4-     4-     4-     8      6      4-     4-    10      4-     4- 
  8   126 :   26     28     35     34     56+    31     28     48     33     35     29     29     28     34     30     28     31     35     32     27- 
  9   210 :   15     22     35     29     84+    24     18     70     26     35     27     21     16-    31     26     23     26     35     26     22  
 10   330 :   15     19     31     24    101+    22     17    101+    23     35     21     20     17     38     22     19     22     35     22     16- 
 11   495 :   12     17     27     18    131+    19     14-   131+    20     33     17     17     14-    35     20     16     18     35     17     14- 
 12   715 :   10     15     19     19    165     16     13-   165     16    141     15     15     13-    32     17     15     16    716+    15     14  
 13   462 :   66    103    126    125    210+    91     94    203    106    126    113    104     92    108    106    102    107    126    112     90- 
 14   792 :   56     78    121    125    330    102     69    316     85    126     86     78     70     82     96     80     84    793+    82     68- 
 15  1287 :   39     61    102    125    461     85     51    461     63    720     63     59     51     81     96     60     64   1288+    63     50- 

Rank  1: Student 13 with score  62
Rank  1: Student 20 with score  62
Rank  3: Student  7 with score  65
Rank  4: Student  2 with score 104
Rank  4: Student 12 with score 104
Rank  4: Student 16 with score 104
=====================================
Rank  7: Student 19 with score 130
Rank  8: Student 11 with score 132
Rank  9: Student 17 with score 135
Rank 10: Student  9 with score 150
Rank 11: Student  6 with score 162
Rank 12: Student 15 with score 177
Rank 13: Student 14 with score 228
Rank 14: Student  4 with score 260
Rank 15: Student  3 with score 282
Rank 16: Student 10 with score 1014
Rank 17: Student  8 with score 1357
Rank 18: Student  5 with score 1407
Rank 19: Student 18 with score 2854

 
Queen Graphs:
 
  #     n :  k 1    k 2    k 3    k 4    k 5    k 6    k 7    k 8    k 9    k10    k11    k12    k13    k14    k15    k16    k17    k18    k19    k20  
  1    16 :    2      2-     2-     2-     3+     3+     2-     2-     2-     2-     2-     2-     2-     3+     2-     2-     2-     2-     2-     2- 
  2    25 :    3      3-     3-     3-     4+     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3-     3- 
  3    36 :    3      3-     4      3-     5+     3-     3-     3-     4      3-     3-     3-     3-     5+     3-     4      4      4      3-     3- 
  4    49 :    4      4-     6+     4-     4-     4-     4-     4-     5      4-     4-     4-     4-     5      4-     4-     5      5      4-     4- 
  5    64 :    5      5-     6+     5-     5-     5-     5-     5-     6+     5-     5-     5-     5-     6+     5-     5-     6+     6+     5-     5- 
  6    81 :    5      5-     6      5-     6      5-     5-     6      7+     6      5-     5-     5-     7+     6      5-     6      6      5-     5- 
  7   100 :    5      5-     8      5-     9+     5-     5-     6      7      7      6      7      5-     8      7      6      8      7      6      5- 
  8   121 :    5      5-     9      5-    10+     5-     6      9     10+     8      7      6      5-    10+     8      5-     7      7      7      5- 
  9   144 :    6      8      9      6-    11+     8      7     11+     8     10      8      8      7     11+     9      7     10      8      7      7  
 10   169 :    7      8     10      8     12+     8      8     12+     8     11      9      9      7-    10     10      7-     9      9      7-     7- 
 11   196 :    8      9     10     11     13+     9      8-    13+     9     12     10      9      8-    12     11     10     11      9      8-     8- 
 12   225 :    9     10     10     12     14     10      9-    14     12     13     11     11      9-    15+    12     10     12     10      9-     9- 
 13   256 :    9     11     12     13     15     12     10     15     11     14     12     11     10     16+    13     11     12     11     10      9- 
 14   289 :    9     13     13     15     16     12     11     16     12     15     14     12     11     17+    14     12     14     13     11     10- 
 15   324 :    9     14     15     16     17+    13     11     17+    14     16     15     13     11     16     15     14     16     12     11     10- 
 16   361 :   10     14     15     17     18     16     12     18     14     17     15     14     12     20+    16     15     17     15     14     11- 
 17   400 :   11     16     15     18     19     16     12-    19     16     18     17     15     12-    21+    16     15     18     16     13     12- 
 18   441 :   11     17     16     19     20     17     14     20     20     19     17     17     13-    23+    20     16     18     15     16     13- 
 19   484 :   12     18     18     20     21     19     14-    21     16     20     19     17     14-    24+    19     18     19     16     15     14- 
 20   529 :   12     19     19     21     22     20     15     22     20     21     20     18     15     25+    25+    18     21     17     17     14- 
 21   576 :   13     20     21     22     23     22     15     23     18     22     22     19     16     27+    24     20     21     19     20     14- 
 22   625 :   13     22     21     23     24     23     17     24     19     24     23     20     17    ---     27+    21     22     19     20     16- 
 23   676 :   14     21     22     24     25     24     17     25     20     88+    23     21     18    ---     29     23     24     22     22     16- 
 24   729 :   14     23     24     25     26     25     18     26     23    157     24     23     18    ---     28     24     26    730+    24     16- 
 25   784 :   15     25     24     26     27     27     19     27     21    226     25     24     19    ---     34     24     26    785+    24     16- 
 26   841 :   15     25     24     27     28     29     20     28     22    295     28     25     20    ---     31     25     27    842+    23     17- 
 27   900 :   15     27     25     28     29     28     21     29     24    368     25     27     21    ---     34     27     26    901+    28     18- 

Rank  1: Student 20 with score  25
Rank  2: Student 13 with score  46
Rank  3: Student  7 with score  47
Rank  4: Student 19 with score  90
Rank  5: Student 12 with score 104
Rank  6: Student  9 with score 107
Rank  6: Student 16 with score 107
Rank  8: Student  2 with score 108
=====================================
Rank  9: Student  3 with score 123
Rank 10: Student  6 with score 127
Rank 11: Student 11 with score 128
Rank 12: Student  4 with score 139
Rank 13: Student 17 with score 146
Rank 14: Student  8 with score 174
Rank 15: Student 15 with score 181
Rank 16: Student  5 with score 182
Rank 17: Student 10 with score 1160
Rank 18: Student 18 with score 3265
Rank 19: Student 14 with score 4681


CSC 425/520 Projects / maintained by Wendy Myrvold / wendym@cs.UVic.ca / revised Nov. 22, 2016