One constraint-propagation engine, run under a dozen ordering and propagator presets, on the same ten corner-pinned variants as the leaderboard. A study of what each knob buys, kept off the headline board because the best preset reaches less than half a contender's score.
The single-core benchmark
leaderboard shows the methods that compete on score. This page shows the rest:
a dozen presets of one constraint-satisfaction engine, plus the naive DFS in its
weaker visit order. They are not a dozen solvers. They are one arc-consistency
core wearing different heads, kept so the exact cost of each classic technique
can be read off a number instead of argued about.
CSP presets, one engine, many knobs
Mean score over ten corner-pinned variants, single core, 60 s each. These are not separate solvers: they are one CSP engine (arc-consistency + a variable/value ordering) run under different presets. The best reaches ~183, less than half a contender's score, so none earns a leaderboard row.
CSP + AC-3naive DFS
Drawing…
Every algorithm across all ten corner variants
One 60 s run per cell. The presets are bimodal: several corners solve near the top, then the same knobs collapse to ~55 on hostile corners.
The presets vary two things: the order the engine assigns cells, and how hard it
propagates before committing. Holding the puzzle and the budget fixed, the score
gap between two presets is the value of that one knob.
Least-constraining-value ordering helps.anjou-gacolor_ac3_lcv reaches a
mean of 114 against the plain anjou-gacolor_ac3 at 76: choosing the value
that rules out the fewest neighbours is worth about 38 points here.
Some knobs are inert at this depth. Three presets (anjou-gacolor_ac3,
anjou-gacolor_ac3_ns1, anjou-verhaard_preferred) produced byte-identical
boards on this puzzle. NS-1 and preferred ordering add nothing at 60 seconds:
the engine never searches deep enough for them to bite.
Border-first ordering is the strongest preset.anjou-border_first_lcv and
anjou-rare_color_first top the sweep at about 183, by committing the
over-constrained frame before the free interior. It is still less than half a
contender's score.
Every preset is bimodal. On a friendly corner arrangement the arc-consistency
search reaches 340 to 349; on a hostile one it collapses to about 55, pinned in a
bad basin it cannot escape inside 60 seconds. The mean sits low because the bad
corners drag it down, and no ordering knob fixes the basin problem. That is the
real story of this family: propagation makes each node well-pruned but expensive,
so the search is strong where the instance is forgiving and helpless where it is
not. The constructive engines on the leaderboard never enter that trap, which is
why a preset at 183 sits on a different page from the leaderboard's contenders,
which top out at 451.
Naive depth-first search with every break allowed is not a CSP preset, but its
visit order belongs to the same lesson. In row-major order
(anjou-naive_rowmajor, on the leaderboard as the baseline) it reaches 365; the
same DFS in spiral visit order (anjou-naive_spiral) collapses to a mean of 78.
The visit-order choice alone costs the naive search nearly 290 points, the same
kind of ordering sensitivity the CSP presets show, at a larger scale.
These presets ran in the same grid as the leaderboard: ten official-puzzle
variants, each with three pinned corner cells, single core, 60 seconds, fixed
seed, one run per variant. Every board is re-scored by the one canonical
matched-edge scorer, never the engine's self-report. The engine, the ten
variants, the committed per-run results and the scripts live under the
experiment's
backing directory,
and just experiments single-core-benchmark reruns the whole grid, contenders
and presets together.