PCPP-Based Reconfiguration Inapproximability: Query Complexity vs. Soundness Gap Trade-offs
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911033327616000 |
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| author | Guruswami, Venkatesan Ren, Xuandi Wu, Kewen |
| author_facet | Guruswami, Venkatesan Ren, Xuandi Wu, Kewen |
| contents | The Reconfiguration Inapproximability Hypothesis (RIH), recently established by Hirahara-Ohsaka (STOC'24) and Karthik-Manurangsi (ECCC'24), studies the hardness of reconfiguring one solution into another in constraint satisfaction problems (CSP) when restricted to approximate intermediate solutions. In this work, we make a tighter connection between RIH's soundness gap and that of probabilistically checkable proofs of proximity (PCPP). Consequently, we achieve an improved trade-off between soundness and query complexity in Gap CSP Reconfiguration. Our approach leverages a parallelization framework, which also appears in some recent parameterized inapproximability results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PCPP-Based Reconfiguration Inapproximability: Query Complexity vs. Soundness Gap Trade-offs Guruswami, Venkatesan Ren, Xuandi Wu, Kewen Computational Complexity The Reconfiguration Inapproximability Hypothesis (RIH), recently established by Hirahara-Ohsaka (STOC'24) and Karthik-Manurangsi (ECCC'24), studies the hardness of reconfiguring one solution into another in constraint satisfaction problems (CSP) when restricted to approximate intermediate solutions. In this work, we make a tighter connection between RIH's soundness gap and that of probabilistically checkable proofs of proximity (PCPP). Consequently, we achieve an improved trade-off between soundness and query complexity in Gap CSP Reconfiguration. Our approach leverages a parallelization framework, which also appears in some recent parameterized inapproximability results. |
| title | PCPP-Based Reconfiguration Inapproximability: Query Complexity vs. Soundness Gap Trade-offs |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2507.01192 |