arXiv:2607. 13219v1 Announce Type: new Abstract: We present cayleyR, an R package for solving permutation puzzles by detecting cycle intersections in Cayley graphs.
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.
arXiv:2607. 10194v1 Announce Type: cross Abstract: We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $\Sigma_{\mathrm{HG}}$.
arXiv:2606. 08904v1 Announce Type: new Abstract: Macro placement is a fundamental step in modern chip physical design, playing a crucial role in determining the solution quality of high-dimensional combinatorial optimization problems.
arXiv:2607. 12026v1 Announce Type: cross Abstract: Finite groups are rigid algebraic objects, whose Cayley graphs expose a rich network geometry through which group-theoretic structure can be measured, compared, and learned.
arXiv:2607. 17481v1 Announce Type: new Abstract: Motif discovery, the search for recurring patterns within a time series, is a core primitive of exploratory data analysis.
Macro placement is a fundamental step in modern chip physical design, playing a crucial role in determining the solution quality of high-dimensional combinatorial optimization problems. Despite recent advancements in machine learning for spatial coordinate determination, the temporal dimension of placement sequencing remains largely governed by static heuristics.
arXiv:2602. 10233v2 Announce Type: replace-cross Abstract: LLM-guided evolutionary computation, most notably AlphaEvolve, has been remarkably successful in discovering novel mathematical constructions by solving challenging optimization problems.
Motif discovery, the search for recurring patterns within a time series, is a core primitive of exploratory data analysis. A pattern, however, is defined by its duration, which analysts rarely know in advance.
arXiv:2608. 08344v1 Announce Type: cross Abstract: Permutation optimization arises whenever the components of a system are fixed but their ordering affects performance.
arXiv:2404. 15616v2 Announce Type: replace-cross Abstract: Grover's search algorithms, including various Partial Grover Searches (PGS), suffer from scaling issues when multiple solutions are sought, as the number of iterations scales with the number of solutions or marked states, making implementation more computationally expensive.
arXiv:2601. 07048v5 Announce Type: replace-cross Abstract: Approximate nearest neighbor search (ANNS) is a core problem in machine learning and information retrieval applications.
arXiv:2512. 20968v2 Announce Type: replace-cross Abstract: Distributed attention is essential for scaling large language models (LLMs) to long contexts, yet existing methods either have limited parallelism or incur high communication costs.