CayleyR: Solving the TopSpin puzzle via cycle intersection

[Submitted on 14 Jul 2026]

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Abstract:We present cayleyR, an R package for solving permutation puzzles by detecting cycle intersections in Cayley graphs. The core algorithm performs an iterative bidirectional search: from both the initial and target permutation states, random operation sequences generate cycles in the Cayley graph of the symmetric group Sn; their intersection yields a connecting path. When no direct intersection is found, a distance-guided bridge selection narrows the gap, and the process repeats. The package targets the TopSpin(n,k) puzzle, whose state space is a Cayley graph of Sn generated by a cyclic shift and a prefix reversal. We describe the mathematical framework, the algorithm, and its implementation, which combines a C++ hash-indexed state store with optional Vulkan GPU acceleration. The software is publicly available on CRAN.

Submission history

From: Yuri Baramykov [view email]
[v1] Tue, 14 Jul 2026 19:28:41 UTC (312 KB)