Finding All Bounded-Length Simple Cycles in a Directed Graph -- Revisited
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909954391146496 |
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| author | Bauernöppel, Frank Sack, Jörg-Rüdiger |
| author_facet | Bauernöppel, Frank Sack, Jörg-Rüdiger |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finding All Bounded-Length Simple Cycles in a Directed Graph -- Revisited Bauernöppel, Frank Sack, Jörg-Rüdiger Data Structures and Algorithms F.2.2 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. |
| title | Finding All Bounded-Length Simple Cycles in a Directed Graph -- Revisited |
| topic | Data Structures and Algorithms F.2.2 |
| url | https://arxiv.org/abs/2512.08392 |