I've been looking at
tarek's mega-collection of minimal 16x16 Sudoku's, with a view to verifying their minimality.
This is a lot more complicated than doing the 2000 puzzles I originally generated for this thread - I deftly avoided the BGS (bad guess syndrome) problem in the generation process, by skipping over any puzzles that took too long for
dSolver16 to solve.
Faced with someone else's output, however, BGS cannot be avoided. For example, just 14 puzzles into the file, I hit one which takes 25s to solve. Others take as little as 0.01s, a pretty big range! And there are bound to be worse cases.
Of course, this is just verifying that the puzzles are valid, not actually proving them minimal …
I'm investigating alternative strategies like those that work for Samurai's - SAT (
*), and the "4CS" method. Meanwhile, I am just continuing with
dSolver16, filtering the batch using guess limits. The first pass with guess limit of 4K completed in 80 minutes. It verified unique solutions for 801,574 puzzles, and gave up on the other 244,460. A fair result, considering ...
A second pass, with 8K guess limit, solved 55,428 of the 244,460 pending cases in 135 minutes. Puzzles pending is now 189,032.
I've repeated this process a couple of times, doubling the guess limit each time, with similar results - I get about 1/4 of the pending puzzles solved, and the overall time goes up by 50-80% for each pass.
When I have identified a small enough pool of unsolved puzzles, I will remove the guess limit and complete the set. The only information to be gained from this exercise (other than confirming that the puzzles are all valid) is the identification of those puzzles which most trouble
dSolver16!
Minimality testing (proper verification of
tarek's batch) will have to wait until I come up with a faster solver option …
* tarek's puzzle #14, takes less than 1s with SAT, so that's a positive sign ...