Biography
I am Cirno Nya(Can Zhou), and I am a graduate student in the Theory Group in the Department of Computer Science and Technology at Nanjing University, where I was fortunate to have Prof. Yitong Yin be my advisor.
Research Interests
- Algorithmic Lovász local lemma
- Counting and Sampling algorithms
- Theoretical Parallel Computing
Education
Nanjing University
2024 - Present
M.S. in Computer Science
Ph.D. in Computer Science
Xidian University
2020 - 2024
B.S. in Computer Science
Publications
Tight Bounds for Sampling q-Colorings via Coupling from the Past
Coauthors:
Tianxing Ding,
Hongyang Liu,
Yitong Yin
Abstract: 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 $\Delta$, the bounding chains of Huber (STOC 1998) provide a systematic framework for efficiently implementing CFTP algorithms within the classical regime $q \ge (1 + o(1))\Delta^2$. This was subsequently improved to $q > 3\Delta$ by Bhandari and Chakraborty (STOC 2020) and to $q \ge (8/3 + o(1))\Delta$ 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 $q \ge 2.5\Delta$, and we present an efficient CFTP algorithm that achieves this asymptotically optimal threshold $q \ge (2.5 + o(1))\Delta$ via an optimal design of bounding chains.
Abstract: 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 $\Delta$, the bounding chains of Huber (STOC 1998) provide a systematic framework for efficiently implementing CFTP algorithms within the classical regime $q \ge (1 + o(1))\Delta^2$. This was subsequently improved to $q > 3\Delta$ by Bhandari and Chakraborty (STOC 2020) and to $q \ge (8/3 + o(1))\Delta$ 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 $q \ge 2.5\Delta$, and we present an efficient CFTP algorithm that achieves this asymptotically optimal threshold $q \ge (2.5 + o(1))\Delta$ via an optimal design of bounding chains.