The New Sudoku Players' Forum

[denis_berthier]

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This is again about my systematic procedure for generating high B puzzles in T&E(1) from minimal puzzles in T&E(3) or T&E(2).

Initially, I thought it was successful due to the continued presence of a tridagon or some degenerate form of it. But my recent results involving non-tridagon puzzles prove it is not the case. I've now run the procedure on 3 sets of minimal puzzles:
1) mith's latest collection mith-TE3 of T&E(3) puzzles (all of which have a non-degenerate tridagon);
2) the collection col-TE2 of mastermins-1-to-15 assembled by coloin (and found mainly by coloin, Hendrik Monard and Paquita), all in T&E(2) with BxB ≥ 7 (all of which have a non-degenerate tridagon);
3) a sub-collection el-TE2 of eleven's tamagotchi high SER puzzles (none of which has a non-degenerate tridagon).

I've measured the throughput as the ratio: output-nb-minimals-in-B12+ / input-nb-min-expands.
I think this is the right quotient to consider (because the effective input is the min-expands, not the minimals).
The results allow no appeal; the success of the procedure can't be due only to the tridagon pattern (though it may play some role within T&E(2)):

- 1.285 B12+ minimal puzzle for each min-expand in mith-TE3
- 7.30 B12+ minimal puzzle for each min-expand in col-TE2
- 2.68 B12+ minimal puzzle for each min-expand in el-TE2

Why T&E(2) puzzles give better results than T&E(3) ones may be because T&E(2) is closer to T&E(1) than T&E(3). It may also be due to the saturation of mith-TE3 by minimisation of the min-expands, which could imply proportionately fewer p1U puzzles (but the stats don't confirm this).
Why, within T&E(2), the puzzles with BxB≥7 give better results, tends to contradict the previous first pseudo-explanation.

Conclusion: clear facts; no real explanation of the results.
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[denis_berthier]

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All the definitions and results reported in this thread - and much more- are now available in the 3rd edition of [HCCS]:
http://forum.enjoysudoku.com/hierarchical-classifications-in-constraint-satisfaction-t42076.html
https://www.lulu.com/shop/denis-berthier/hierarchical-classifications-in-constraint-satisfaction-third-edition/paperback/product-4587d42.html?page=1&pageSize=4

One of the topics not discussed here is the (1+BRT) distance of a T&E(n) puzzle to the T&E(n) border. Indeed several notions of distance can be defined, including the most natural one related to the shortest (1+BRT)-expansion paths.

One apparently surprising result for the latter is, whereas the maximum length of expansion paths increases drastically from T&E(3) to T&E(1), it is not the case for the thickness of the T&E(n) domains.
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[denis_berthier]

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All the data relevant to the exploration of the T&E(3) kingdom via (1+BRT)-expansion of T&E(3) minimal puzzles, as described in [HCCS3], have been published:
All-time latest release: https://doi.org/10.5281/zenodo.17500794
Download all (2.5 GB), unzip and see the README.md file for details.

Similar data for the T&E(2) and T&E(1) kingdoms will be published soon.
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[denis_berthier]

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All the data relevant to the exploration of the T&E(1) kingdom via (1+BRT)-expansion of T&E(1) minimal puzzles, as described in [HCCS3], have been published:
https://doi.org/10.5281/zenodo.17505247
Download all (1 GB), unzip (=> 20 GB) and see the README.md file for details.

Similar data for the T&E(2) kingdom will be published later.
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[denis_berthier]

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All the data relevant to the exploration of the pre-tridagon, low BxB part of the T&E(2) kingdom via (1+BRT)-expansion of T&E(2) minimal puzzles, as described in [HCCS3], have been published:
https://doi.org/10.5281/zenodo.17510758
Download all (500 MB), unzip (=> 10 GB) and see the README.md file for details.

Similar data for the post-tridagon, high BxB part of the T&E(2) kingdom will be published later.
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[denis_berthier]

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Finally, all the data relevant to the exploration of the post-tridagon, high BxB part of the T&E(2) kingdom via (1+BRT)-expansion of T&E(2) minimal puzzles, as described in [HCCS3], have been published:https://zenodo.org/records/17529657
Download all, unzip and see the README.md file for details.

Note that additional data used in [HCCS3] had already been published:
https://github.com/denis-berthier/Controlled-bias_Sudoku_generator_and_collection
https://github.com/denis-berthier/Sudoku-classif
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[denis_berthier]

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[Moved from the "BxB classification" thread.
The collection referred to was defined here: http://forum.enjoysudoku.com/the-bxb-classification-of-t-e-2-puzzles-t41922-375.html and next posts.]

After analysing Paquita's new high BxB puzzles (as collated by coloin) by my (1+BRT)-expansion technique, the record of the longest expansion path in T&E(2) is beaten: 13 (instead of 12 previously):

Code: Select all

.23...78.45.78..237.8...5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 43c +BRT -> --p13EU
.23...78.45.78..237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 42c +p13
.23...78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 41c +BRT -> --p12EU
.23...78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 41c +p12
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 40c +BRT -> --p11EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 40c +p11
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...9..1.8... 39c +BRT -> --p10EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...9..1.8... 39c +p10
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3......1.8... 38c +BRT -> --p9EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3......1.8... 38c +p9
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 37c +BRT -> --p8EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 37c +p8
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 36c +BRT -> --p7EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 36c +p7
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..974..284...3......1.8... 35c +BRT -> --p6EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..974..284...3......1.8... 35c +p6
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9.4..284...3......1.8... 34c +BRT -> --p5EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9.4..284...3......1.8... 34c +p5
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.7...9.4..284...3......1.8... 33c +BRT -> --p4EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.7...9.4..284...3......1.8... 33c +p4
.2....7..45.7...237.....5.42.5..73..37...2.58.84..52.7...9.4..284...3......1.8... 32c +BRT -> --p3EU
.2....7..45.7...237.....5.42....73..37...2.58.84..52.7...9.4..284...3......1.8... 31c +p3
.2....7..45.7...237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 30c +BRT -> --p2EU
.2....7..45.7...237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 30c +p2
.2....7..45.....237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 29c +BRT -> --p1EU
.2....7..45.....237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 29c +p1
.2.......45.....237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 28c +BRT -> --p0EU
.2.......45.....237.....5.4.....73..37...2.58.84..5..7...9.4..284...3......1.8... 27c +p0
computation-time = 2.68s

There are actually 3 puzzles in the collection with such a path. The upper terminations of the paths are related to each other by permutation of clues in some UR1.

[Edit]: as noted by an attentive reader of [HCCS3], the T&E(2) record is not broken; it was already 13, as mentioned in [HCCS3, section 7.2.3]. What's broken is the record for the part of T&E(2) with BxB ≥ 7.
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