CayleyR: Solving the TopSpin puzzle via cycle intersection
Quick Answer
This paper shows that The cayleyR R package efficiently solves the TopSpin(n,k) puzzle using cycle intersections in Cayley graphs.
Quick Take
It employs a bidirectional search algorithm that generates cycles from both initial and target states, optimizing the search with distance-guided bridge selection and optional GPU acceleration. The software is publicly available on CRAN.
Key Points
- cayleyR targets the TopSpin(n,k) permutation puzzle using Cayley graphs.
- The algorithm combines bidirectional search with cycle intersection detection.
- Distance-guided bridge selection improves search efficiency when direct intersections are absent.
- The package integrates a C++ hash-indexed state store for performance.
- Publicly available on CRAN for researchers and developers.
Paper Resources
📖 Reader Mode
~2 min readAbstract: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.
| Comments: | 17 pages, 2 figures |
| Subjects: | Artificial Intelligence (cs.AI) |
| MSC classes: | 20B40, 05C25, 68W05 |
| ACM classes: | F.2.2; I.2.8; G.2.1 |
| Cite as: | arXiv:2607.13219 [cs.AI] |
| (or arXiv:2607.13219v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2607.13219 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yuri Baramykov [view email]
[v1]
Tue, 14 Jul 2026 19:28:41 UTC (312 KB)
— Originally published at arxiv.org
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