{"ID":2831103,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.08392","arxiv_id":"2512.08392","title":"Finding All Bounded-Length Simple Cycles in a Directed Graph -- Revisited","abstract":"In 2021, Gupta and Suzumura proposed a novel algorithm for enumerating all bounded-length simple cycles in directed graphs. In this work, we present concrete examples demonstrating that the proposed algorithm fails to enumerate certain valid cycles. Via these examples, we perform a detailed analysis pinpointing the specific points at which the proofs exhibit logical gaps. Furthermore, we propose a corrected formulation that resolves these issues while preserving the desirable property that the algorithm's computational complexity remains $O((c + 1) \\cdot k \\cdot (n + e))$ where $c$ is the number of simple cycles of a specified maximum length $k$, and $n$ and $e$ the number of graph nodes and edges respectively.","short_abstract":"In 2021, Gupta and Suzumura proposed a novel algorithm for enumerating all bounded-length simple cycles in directed graphs. In this work, we present concrete examples demonstrating that the proposed algorithm fails to enumerate certain valid cycles. Via these examples, we perform a detailed analysis pinpointing the spe...","url_abs":"https://arxiv.org/abs/2512.08392","url_pdf":"https://arxiv.org/pdf/2512.08392v2","authors":"[\"Frank Bauernöppel\",\"Jörg-Rüdiger Sack\"]","published":"2025-12-09T09:21:41Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}