Lower Bounds for Testing Directed Acyclicity in the Unidirectional Bounded-Degree Model
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914474254925824 |
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| author | Yoshida, Yuichi |
| author_facet | Yoshida, Yuichi |
| contents | We study property testing of directed acyclicity in the unidirectional bounded-degree oracle model, where a query to a vertex reveals its outgoing neighbors. We prove that there exist absolute constants $d_0\in\mathbb{N}$ and $\varepsilon>0$ such that for every constant $d\ge d_0$, any one-sided $\varepsilon$-tester for acyclicity on $n$-vertex digraphs of maximum outdegree at most $d$ requires $\widetildeΩ(n^{2/3})$ queries. This improves the previous $\widetildeΩ(n^{5/9})$ lower bound for one-sided testing of acyclicity in the same model. We also prove that, under the same degree assumption, any two-sided $\varepsilon$-tester requires $Ω(\sqrt n)$ queries, improving the previous $Ω(n^{1/3})$ lower bound. We further prove an $Ω(n)$ lower bound for tolerant testing for some absolute constant outdegree bound $d$ by reduction from bounded-degree $3$-colorability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13577 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lower Bounds for Testing Directed Acyclicity in the Unidirectional Bounded-Degree Model Yoshida, Yuichi Data Structures and Algorithms We study property testing of directed acyclicity in the unidirectional bounded-degree oracle model, where a query to a vertex reveals its outgoing neighbors. We prove that there exist absolute constants $d_0\in\mathbb{N}$ and $\varepsilon>0$ such that for every constant $d\ge d_0$, any one-sided $\varepsilon$-tester for acyclicity on $n$-vertex digraphs of maximum outdegree at most $d$ requires $\widetildeΩ(n^{2/3})$ queries. This improves the previous $\widetildeΩ(n^{5/9})$ lower bound for one-sided testing of acyclicity in the same model. We also prove that, under the same degree assumption, any two-sided $\varepsilon$-tester requires $Ω(\sqrt n)$ queries, improving the previous $Ω(n^{1/3})$ lower bound. We further prove an $Ω(n)$ lower bound for tolerant testing for some absolute constant outdegree bound $d$ by reduction from bounded-degree $3$-colorability. |
| title | Lower Bounds for Testing Directed Acyclicity in the Unidirectional Bounded-Degree Model |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2604.13577 |