Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a tighter analysis of two previous approximation algorithms, improving their approximation guarantees from 4 to 3. Moreover, we show that both algorithms can be derandomized in a surprisingly simple way, by greedily taking a vertex of maximum degree in an auxiliary graph and forming a cluster around it. One of these algorithms relies on solving a linear program. Our final contribution is to design a new and purely combinatorial approach for doing so that is far more scalable in theory and practice.

翻译：簇删除是一个NP难的图聚类目标，在计算生物学和社交网络分析中具有应用，其目标是通过删除最少数量的边将图划分为团。我们首先对两种已有的近似算法进行了更紧致的分析，将其近似比从4提升至3。此外，我们展示这两种算法可以通过一种惊人的简单方式实现去随机化：在辅助图中贪心地选取最大度顶点并围绕其构建簇。其中一种算法依赖于求解线性规划。我们的最终贡献是设计了一种全新的纯组合方法来实现该求解，该方法在理论和实践中都具有显著更高的可扩展性。