AGENTIC-SYSTEMSJuly 16, 20261 min read

CayleyR: Solving the TopSpin puzzle via cycle intersection

Researchers have introduced cayleyR, an R package designed to solve complex permutation puzzles like TopSpin. By combining Cayley graph theory, bidirectional search, and Vulkan GPU acceleration, this tool opens new avenues for combinatorial optimization.

Computer Science > Artificial Intelligence

Title:CayleyR: Solving the TopSpin puzzle via cycle intersection

View PDF HTML (experimental)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.

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Source: arXiv cs.AI Recent

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