Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2511.04982 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908664648957952 |
|---|---|
| author | Ding, Tianxing Liu, Hongyang Yin, Yitong Zhou, Can |
| author_facet | Ding, Tianxing Liu, Hongyang Yin, Yitong Zhou, Can |
| contents | The Coupling from the Past (CFTP) paradigm is a canonical method for perfect sampling. For uniform sampling of proper $q$-colorings in graphs with maximum degree $Δ$, the bounding chains of Huber (STOC 1998) provide a systematic framework for efficiently implementing CFTP algorithms within the classical regime $q \ge (1 + o(1))Δ^2$. This was subsequently improved to $q > 3Δ$ by Bhandari and Chakraborty (STOC 2020) and to $q \ge (8/3 + o(1))Δ$ by Jain, Sah, and Sawhney (STOC 2021).
In this work, we establish the asymptotically tight threshold for bounding-chain-based CFTP algorithms for graph colorings. We prove a lower bound showing that all such algorithms satisfying the standard contraction property require $q \ge 2.5Δ$, and we present an efficient CFTP algorithm that achieves this asymptotically optimal threshold $q \ge (2.5 + o(1))Δ$ via an optimal design of bounding chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tight Bounds for Sampling q-Colorings via Coupling from the Past Ding, Tianxing Liu, Hongyang Yin, Yitong Zhou, Can Data Structures and Algorithms The Coupling from the Past (CFTP) paradigm is a canonical method for perfect sampling. For uniform sampling of proper $q$-colorings in graphs with maximum degree $Δ$, the bounding chains of Huber (STOC 1998) provide a systematic framework for efficiently implementing CFTP algorithms within the classical regime $q \ge (1 + o(1))Δ^2$. This was subsequently improved to $q > 3Δ$ by Bhandari and Chakraborty (STOC 2020) and to $q \ge (8/3 + o(1))Δ$ by Jain, Sah, and Sawhney (STOC 2021). In this work, we establish the asymptotically tight threshold for bounding-chain-based CFTP algorithms for graph colorings. We prove a lower bound showing that all such algorithms satisfying the standard contraction property require $q \ge 2.5Δ$, and we present an efficient CFTP algorithm that achieves this asymptotically optimal threshold $q \ge (2.5 + o(1))Δ$ via an optimal design of bounding chains. |
| title | Tight Bounds for Sampling q-Colorings via Coupling from the Past |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2511.04982 |