- Code: Select all
20 17
294 18
32748 19
12141180 20
20 17
294 18
32748 19
12141180 20
+----+-----------+--------------+------------+
| Cl | Count | E(nr/grid) | E(rel err) |
+----+-----------+--------------+------------+
| 17 | 24 | 2.1983e+001 | 39.97% |
| 18 | 56 | 2.9844e+002 | 26.96% |
| 19 | 963 | 3.2332e+004 | 6.60% |
| 20 | 52345 | 1.2107e+007 | 0.83% |
+----+-----------+--------------+------------+ [blue]
Afmob wrote:As for the results, one can often find situations where one method is better than the other and vice versa.
Afmob wrote:For example if I look at the relative error for the number of 22 clue minimals you got a relative error of 1.23% and blue got about 0.05% which is a major difference. Note that I choose blue's results since they have no sample error and the computation time is not as large is mine was.
denis_berthier wrote:Starting from only 100k (subset) or 10k (superset) grids sets a bound on the precision of any calculations you can do.
denis_berthier wrote:Afmob wrote:For example if I look at the relative error for the number of 22 clue minimals you got a relative error of 1.23% and blue got about 0.05% which is a major difference. Note that I choose blue's results since they have no sample error and the computation time is not as large is mine was.
As I said in my previous post, if we concentrate on low clues, the controlled-bias generator can be made drastically much faster by increasing the number of clues deleted from the start without checking if the resulting puzzle is minimal.
Afmob wrote:denis_berthier wrote:Starting from only 100k (subset) or 10k (superset) grids sets a bound on the precision of any calculations you can do.
Please read my post again. I did not only use 100k or 10k grids but about 60.2 billion (subset) and 2.1 billion (superset) different random unbiased grids otherwise I wouldn't have made this large computation. The only sample error I introduce is that I use each grid 10 times so that the generator takes up only a small amount of the computation time.
blue wrote:denis_berthier wrote:Afmob wrote:For example if I look at the relative error for the number of 22 clue minimals you got a relative error of 1.23% and blue got about 0.05% which is a major difference. Note that I choose blue's results since they have no sample error and the computation time is not as large is mine was.
As I said in my previous post, if we concentrate on low clues, the controlled-bias generator can be made drastically much faster by increasing the number of clues deleted from the start without checking if the resulting puzzle is minimal.
I'm not sure how low you mean when you say "low clues", but if we focused on the size 22 estimate,
A fairer summary would be that subset/superset methods are advantageous in the computation of "cheap" random variables, whereas path probing (controlled bias generation) is advantageous for "expensive" random variables. Further, subset/superset methods are especially powerful in the tails of the distribution, whereas path probing is competitive (or better if the random variable is sufficiently expensive) around the centre or in computation of the overall mean.denis_berthier wrote:... to compute the distributions of various random variables - a goal for which the subset/superset method is totally unfit.
Red Ed wrote:A fairer summary would be that subset/superset methods are advantageous in the computation of "cheap" random variables, whereas path probing (controlled bias generation) is advantageous for "expensive" random variables.denis_berthier wrote:... to compute the distributions of various random variables - a goal for which the subset/superset method is totally unfit.
Red Ed wrote:subset/superset methods are especially powerful in the tails of the distribution
denis_berthier wrote:Generation is a one shot business. And, considering the numbers of puzzles generated by each method, I'd say that this business is over (and indeed much beyond what's useful) as long as distributions of RVs are concerned.
Computation time: 31x72 hours
235,091 samples
235,091 size 3 subsets
814 valid minimal puzzles
+----+-------+------------+----------------+
| Cl | Count | E(nr/grid) | E(rel err)*100 |
+----+-------+------------+----------------+
| 18 | 814 | 3.620e-01 | 5.813e+00 |
+----+-------+------------+----------------+