给定度简单图均匀采样的并行全局边切换
Parallel Global Edge Switching for the Uniform Sampling of Simple Graphs with Prescribed Degrees
摘要：
匹配给定度序列的简单图的均匀抽样是网络科学中的一个重要工具，例如构造图生成器或零模型。在这里，边缘切换马尔可夫链（ES-MC）是一种常见的选择。给定一个具有所需度序列的任意简单图，ES-MC进行大量的小变化，称为边切换，最终获得均匀的样本。在实践中，合理的短运行有效地产生近似均匀的样本。在这项工作中，我们研究了并行执行边缘开关的问题。我们讨论了ES-MC的并行化，但发现这种方法存在边缘交换机之间复杂的依赖关系。为此，我们提出了全局边缘切换马尔可夫链（G-ES-MC），一个更简单的依赖ES-MC变体。我们证明了G-ES-MC收敛于均匀分布，并设计了ES-MC和G-ES-MC的共享内存并行算法。在实证评估中，我们提供的证据表明，G-ES-MC需要不超过ES-MC（往往更少）的开关，并证明我们的并行G-ES-MC实现的效率和可扩展性。
英文摘要：
The uniform sampling of simple graphs matching a prescribed degree sequence is an important tool in network science, e.g. to construct graph generators or null-models. Here, the Edge Switching Markov Chain (ES-MC) is a common choice. Given an arbitrary simple graph with the required degree sequence, ES-MC carries out a large number of small changes, called edge switches, to eventually obtain a uniform sample. In practice, reasonably short runs efficiently yield approximate uniform samples. In this work, we study the problem of executing edge switches in parallel. We discuss parallelizations of ES-MC, but find that this approach suffers from complex dependencies between edge switches. For this reason, we propose the Global Edge Switching Markov Chain (G-ES-MC), an ES-MC variant with simpler dependencies. We show that G-ES-MC converges to the uniform distribution and design shared-memory parallel algorithms for ES-MC and G-ES-MC. In an empirical evaluation, we provide evidence that G-ES-MC requires not more switches than ES-MC (and often fewer), and demonstrate the efficiency and scalability of our parallel G-ES-MC implementation.
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