Generality of small-support pathfinding methods

Determine whether small-support elements can be effectively found from arbitrary given generators, thereby establishing whether small-support methods generalize beyond particular choices of generators.

Background

Small-support methods first derive permutations affecting only a few positions and then use them as new generators for beam search. They are effective for some very large groups and puzzles, but their applicability to arbitrary generating sets is not established. The paper identifies effective discovery of such elements from the original generators as the central unresolved issue concerning the method’s generality.

References

however it is unclear whether one can effectively find small support elements from given generators, thus making unclear the generality of "small support methods".

— CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphs  (2502.18663 - Chervov et al., 25 Feb 2025) in Section 2.4, subsection “Non-optimal pathfinding: \"small support\" Kaggle Santa 2023 methods (generality issue)”