海量图上最大团问题的快速算法及其在重叠社区检测中的应用

Q3 Mathematics Internet Mathematics Pub Date : 2014-11-26 DOI:10.1080/15427951.2014.986778
B. Pattabiraman, Md. Mostofa Ali Patwary, A. Gebremedhin, W. Liao, A. Choudhary
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引用次数: 50

摘要

最大团问题是一个众所周知的np困难问题,在数据挖掘、网络分析、信息检索以及与万维网相关的许多其他领域都有应用。有几种算法可以解决这个问题,它们对于某些类型的图具有可接受的运行时间,但其中许多算法对于大规模图是不可行的。我们提出了一种新的精确算法,该算法采用了新颖的修剪技术,能够快速地在非常大的稀疏图中找到最大的团。在不同种类的合成图和真实世界的图上进行的大量实验表明,我们的新算法可以比现有算法快几个数量级。我们还提出了一种启发式算法,它的运行速度比精确算法快几个数量级,同时提供了最优或接近最优的解决方案。我们举例说明了算法在开发网络中重叠社区检测方法中的一个简单应用。
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Fast Algorithms for the Maximum Clique Problem on Massive Graphs with Applications to Overlapping Community Detection
The maximum clique problem is a well-known NP-hard problem with applications in data mining, network analysis, information retrieval, and many other areas related to the World Wide Web. There exist several algorithms for the problem, with acceptable runtimes for certain classes of graphs, but many of them are infeasible for massive graphs. We present a new exact algorithm that employs novel pruning techniques and is able to find maximum cliques in very large, sparse graphs quickly. Extensive experiments on different kinds of synthetic and real-world graphs show that our new algorithm can be orders of magnitude faster than existing algorithms. We also present a heuristic that runs orders of magnitude faster than the exact algorithm while providing optimal or near-optimal solutions. We illustrate a simple application of the algorithms in developing methods for detection of overlapping communities in networks.
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Internet Mathematics
Internet Mathematics Mathematics-Applied Mathematics
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