As a relaxation of clique in graph theory, k-plex is a powerful tool for analyzing social networks and identifying cohesive structures in graphs. Recently, more and more researchers have concentrated on the algorithms for the maximum k-plex problem. Among those algorithms, a branch-and-bound algorithm proposed very recently shows a good performance on solving large sparse graphs, but does not work well on social networks. In this paper, we propose two novel vertex selection heuristic strategies for branching. The first one employs historical information of vertex reduction, and the second one is a combination of the first heuristic and the degree-based approach. Intensive experiments on Facebook benchmark show that the algorithm combining our heuristics outperforms the state-of-the-art algorithms.

中文翻译：

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最大 k-Plex 问题的分支定界算法中的顶点选择启发式

作为图论中 clique 的一种放松，k-plex 是分析社交网络和识别图中内聚结构的强大工具。最近，越来越多的研究人员将注意力集中在最大 k-plex 问题的算法上。在这些算法中，最近提出的分支定界算法在解决大型稀疏图方面表现出良好的性能，但在社交网络上效果不佳。在本文中，我们提出了两种新颖的用于分支的顶点选择启发式策略。第一个使用顶点减少的历史信息，第二个是第一个启发式和基于度数的方法的组合。Facebook 基准上的密集实验表明，结合我们的启发式算法的算法优于最先进的算法。