一种基于台球轨迹和模拟退火的实用体积估计算法

Q2 Mathematics Journal of Experimental Algorithmics Pub Date : 2023-03-03 DOI:10.1145/3584182
Apostolos Chalkis, I. Emiris, Vissarion Fisikopoulos
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引用次数: 3

摘要

当凸多面体以三种不同的表示形式给出时,我们解决了有效近似凸多面体体积的问题:已被广泛研究的H-多面体、V-多面体和zonotopes(Z-多面体)。我们设计了一种新颖实用的多相蒙特卡罗算法,该算法利用了基于台球轨迹的随机行走,以及一种新的经验收敛测试和自适应凸体的模拟退火调度。在调整了我们提出的方法的几个参数后,我们使用包含Birkhoff多面体和结构生物学多面体的丰富数据集,对我们的调整算法进行了详细的实验评估。我们的开源实现解决了迄今为止难以解决的问题,提供了第一个在中等硬件上扩展H多面体数千维和V和Z多面体数百维的软件。最后,我们展示了我们的软件在评估Z-多面体近似。
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A practical algorithm for volume estimation based on billiard trajectories and simulated annealing
We tackle the problem of efficiently approximating the volume of convex polytopes, when these are given in three different representations: H-polytopes, which have been studied extensively, V-polytopes, and zonotopes (Z-polytopes). We design a novel practical Multiphase Monte Carlo algorithm that leverages random walks based on billiard trajectories, as well as a new empirical convergence tests and a simulated annealing schedule of adaptive convex bodies. After tuning several parameters of our proposed method, we present a detailed experimental evaluation of our tuned algorithm using a rich dataset containing Birkhoff polytopes and polytopes from structural biology. Our open-source implementation tackles problems that have been intractable so far, offering the first software to scale up in thousands of dimensions for H-polytopes and in the hundreds for V- and Z-polytopes on moderate hardware. Last, we illustrate our software in evaluating Z-polytope approximations.
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来源期刊
Journal of Experimental Algorithmics
Journal of Experimental Algorithmics Mathematics-Theoretical Computer Science
CiteScore
3.10
自引率
0.00%
发文量
29
期刊介绍: The ACM JEA is a high-quality, refereed, archival journal devoted to the study of discrete algorithms and data structures through a combination of experimentation and classical analysis and design techniques. It focuses on the following areas in algorithms and data structures: ■combinatorial optimization ■computational biology ■computational geometry ■graph manipulation ■graphics ■heuristics ■network design ■parallel processing ■routing and scheduling ■searching and sorting ■VLSI design
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