Journal of Software
1000-9825
1
14
10.13328/j.cnki.jos.006926
article
面向超图数据的最大独立集算法
Maximum Independent Set Algorithm for Hypergraph Data
超图是普通图的泛化表示, 在许多应用领域都很常见, 包括互联网、生物信息学和社交网络等. 独立集问题是图分析领域的一个基础性研究问题, 传统的独立集算法大多都是针对普通图数据, 如何在超图数据上实现高效的最大独立集挖掘是一个亟待解决的问题. 针对这一问题, 提出一种超图独立集的定义. 首先分析超图独立集搜索的两个特性, 然后提出一种基于贪心策略的基础算法. 接着提出一种超图近似最大独立集搜索的剪枝框架即精确剪枝与近似剪枝相结合, 以精确剪枝策略缩小图的规模, 以近似剪枝策略加快搜索速度. 此外, 还提出4种高效的剪枝策略, 并对每种剪枝策略进行理论证明. 最后, 通过在10个真实超图数据集上进行实验, 结果表明剪枝算法可以高效地搜索到更接近于真实结果的超图最大独立集.
Hypergraphs are generalized representations of ordinary graphs, which are common in many application areas, including the Internet, bioinformatics, and social networks. The independent set problem is a fundamental research problem in the field of graph analysis. Most of the traditional independent set algorithms are targeted for ordinary graph data, and how to achieve efficient maximum independent set mining on hypergraph data is an urgent problem to be solved. To address this problem, this study proposes a definition of hypergraph independent sets. Firstly, two properties of hypergraph independent set search are analyzed, and then a basic algorithm based on the greedy strategy is proposed. Then a pruning framework for hypergraph approximate maximum independent set search is proposed, i.e., a combination of exact pruning and approximate pruning, which reduces the size of the graph by the exact pruning strategy and speeds up the search by the approximate pruning strategy. In addition, four efficient pruning strategies are proposed in this study, and a theoretical proof of each pruning strategy is presented. Finally, experiments are conducted on 10 real hypergraph data sets, and the results show that the pruning algorithm can efficiently search for hypergraph maximum independent sets that are closer to the real results.
超图;最大独立集;启发式算法
hypergraph;maximum independent set;heuristic algorithm
徐兰天,李荣华,戴永恒,王国仁
XU Lan-Tian, LI Rong-Hua, DAI Yong-Heng, WANG Guo-Ren
jos/article/abstract/6926