子集问题硬枚举变量的细粒度搜索空间分类
Fine-grained Search Space Classification for Hard Enumeration Variants of Subset Problems
摘要：
我们提出了一个简单，功能强大，灵活的机器学习框架（i）减少计算困难的枚举子集问题的变种的搜索空间和（ii）增强现有的国家的最先进的解决方案与信息提示所产生的输入分布。我们实例化我们的框架，列出所有最大的集团在一个图中，在网络分析，数据采掘和计算生物学的中心问题的问题。我们证明了我们的方法在具有数百万个顶点和边的真实网络上的实用性，不仅保留了所有的最佳解决方案，而且还积极修剪输入实例大小，从而使最先进的算法加速数倍。最后，我们探讨了我们提出的框架的可扩展性和鲁棒性的限制，这表明监督学习是可行的，在实践中解决NP难问题。
英文摘要：
We propose a simple, powerful, and flexible machine learning framework for (i) reducing the search space of computationally difficult enumeration variants of subset problems and (ii) augmenting existing state-of-the-art solvers with informative cues arising from the input distribution. We instantiate our framework for the problem of listing all maximum cliques in a graph, a central problem in network analysis, data mining, and computational biology. We demonstrate the practicality of our approach on real-world networks with millions of vertices and edges by not only retaining all optimal solutions, but also aggressively pruning the input instance size resulting in several fold speedups of state-of-the-art algorithms. Finally, we explore the limits of scalability and robustness of our proposed framework, suggesting that supervised learning is viable for tackling NP-hard problems in practice.
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