Technology Category
Search and Optimization: Sampling/Simulation-based SearchConstraint Satisfaction and Optimization: Distributed CSP/OptimizationMachine Learning: Probabilistic Circuits and Graphical Models
Work-Efficient Parallel Counting via Sampling
🤖 AI Summary
This paper addresses the problem of efficiently approximating the partition function of Gibbs distributions in parallel. Existing algorithms face a fundamental trade-off between total work and parallel depth. We propose the first counting-to-sampling reduction framework that simultaneously achieves near-optimal total work—approaching the information-theoretic lower bound—and logarithmic parallel depth. Methodologically, we build upon the simulated annealing paradigm, designing an adaptive temperature schedule and a parallel sampling verification mechanism to ensure work efficiency. Our theoretical contribution is the first work-efficient parallel counting algorithm for both the hardcore model and the Ising model within their uniqueness regimes. This overcomes the inherent limitations of prior approaches: non-adaptive algorithms suffer from suboptimal work complexity, while adaptive ones are inherently sequential. Our framework thus unifies asymptotic optimality in work with high parallelism, establishing a new state of the art in parallel approximate counting.
Technology Category
Application Category
📝 Abstract
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: $ullet$ classic non-adaptive (parallel) algorithms with sub-optimal cost (Dyer-Frieze-Kannan '89; Bez'akov'a-v{S}tefankoviv{c}-Vazirani-Vigoda '08); $ullet$ adaptive (sequential) algorithms with near-optimal cost (v{S}tefankoviv{c}-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.
Problem
Research questions and friction points this paper is trying to address.
Efficient parallel counting via sampling for Gibbs distributions
Reduction from counting to sampling with near-optimal work
Work-efficient algorithms for hardcore and Ising models
Innovation
Methods, ideas, or system contributions that make the work stand out.
Parallel counting via efficient sampling
Logarithmic depth near-optimal work
Hardcore and Ising models coverage
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