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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2512.20598 |
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| _version_ | 1866908730620116992 |
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| author | Date, Vinicius T. V. Zatesko, Leandro M. |
| author_facet | Date, Vinicius T. V. Zatesko, Leandro M. |
| contents | In the field of compressed string indexes, recent work has introduced suffixient sets and their corresponding repetitiveness measure $χ$. In particular, researchers have explored its relationship to other repetitiveness measures, notably $r$, the number of runs in the Burrows--Wheeler Transform (BWT) of a string. Navarro et al. (2025) proved that $χ\leq 2r$, although empirical results by Cenzato et al. (2024) suggest that this bound is loose, with real data bounding $χ$ by around $1.13r$ to $1.33r$ when the size of the alphabet is $σ= 4$. To better understand this gap, we present two cases for the asymptotic tightness of the $χ\leq 2r$ bound: a general construction for arbitrary $σ$ values, and a binary alphabet case, consisting of de Bruijn sequences constructed by linear-feedback shift registers (LFSRs) from primitive polynomials over $\mathbb{F}_2$. The second is a novel characterization of which de Bruijn sequences achieve the literature run-minimal pattern for the cyclic BWT. Moreover, we show that de Bruijn sequences fail to close the gap for $σ\geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the near-tightness of $χ\leq 2r$: a general $σ$-ary construction and a binary case via LFSRs Date, Vinicius T. V. Zatesko, Leandro M. Data Structures and Algorithms 68R15 (Primary), 68W32 (Secondary) F.2.2; E.4 In the field of compressed string indexes, recent work has introduced suffixient sets and their corresponding repetitiveness measure $χ$. In particular, researchers have explored its relationship to other repetitiveness measures, notably $r$, the number of runs in the Burrows--Wheeler Transform (BWT) of a string. Navarro et al. (2025) proved that $χ\leq 2r$, although empirical results by Cenzato et al. (2024) suggest that this bound is loose, with real data bounding $χ$ by around $1.13r$ to $1.33r$ when the size of the alphabet is $σ= 4$. To better understand this gap, we present two cases for the asymptotic tightness of the $χ\leq 2r$ bound: a general construction for arbitrary $σ$ values, and a binary alphabet case, consisting of de Bruijn sequences constructed by linear-feedback shift registers (LFSRs) from primitive polynomials over $\mathbb{F}_2$. The second is a novel characterization of which de Bruijn sequences achieve the literature run-minimal pattern for the cyclic BWT. Moreover, we show that de Bruijn sequences fail to close the gap for $σ\geq 3$. |
| title | On the near-tightness of $χ\leq 2r$: a general $σ$-ary construction and a binary case via LFSRs |
| topic | Data Structures and Algorithms 68R15 (Primary), 68W32 (Secondary) F.2.2; E.4 |
| url | https://arxiv.org/abs/2512.20598 |