Work-Efficient Parallel Counting via Sampling
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911567984984064 |
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| author | Liu, Hongyang Yin, Yitong Zhang, Yiyao |
| author_facet | Liu, Hongyang Yin, Yitong Zhang, Yiyao |
| contents | A canonical approach to approximating the partition function of a Gibbs distribution via sampling is simulated annealing. This method has led to efficient reductions from counting to sampling, including:
$\bullet$ classic non-adaptive (parallel) algorithms with sub-optimal cost (Dyer-Frieze-Kannan '89; Bezáková-Štefankovič-Vazirani-Vigoda '08);
$\bullet$ adaptive (sequential) algorithms with near-optimal cost (Štefankovič-Vempala-Vigoda '09; Huber '15; Kolmogorov '18; Harris-Kolmogorov '24).
We present an algorithm that achieves both near-optimal total work and efficient parallelism, providing a reduction from counting to sampling with logarithmic depth and near-optimal work. As consequences, we obtain work-efficient parallel counting algorithms for several important models, including the hardcore and Ising models within the uniqueness regime. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_09719 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Work-Efficient Parallel Counting via Sampling Liu, Hongyang Yin, Yitong Zhang, Yiyao Data Structures and Algorithms Computational Complexity Distributed, Parallel, and Cluster Computing A canonical approach to approximating the partition function of a Gibbs distribution via sampling is simulated annealing. This method has led to efficient reductions from counting to sampling, including: $\bullet$ classic non-adaptive (parallel) algorithms with sub-optimal cost (Dyer-Frieze-Kannan '89; Bezáková-Štefankovič-Vazirani-Vigoda '08); $\bullet$ adaptive (sequential) algorithms with near-optimal cost (Štefankovič-Vempala-Vigoda '09; Huber '15; Kolmogorov '18; Harris-Kolmogorov '24). We present an algorithm that achieves both near-optimal total work and efficient parallelism, providing a reduction from counting to sampling with logarithmic depth and near-optimal work. As consequences, we obtain work-efficient parallel counting algorithms for several important models, including the hardcore and Ising models within the uniqueness regime. |
| title | Work-Efficient Parallel Counting via Sampling |
| topic | Data Structures and Algorithms Computational Complexity Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2408.09719 |