We study the problem of clustering the vertices of a weighted hypergraph such that on average the vertices of each edge can be covered by a small number of clusters. This problem has many applications, such as for designing medical tests, clustering files on disk servers, and placing network services on servers. The edges of the hypergraph model groups of items that are likely to be needed together, and the optimization criteria that we use can be interpreted as the average delay (or cost) to serve the items of a typical edge. We describe and analyze algorithms for this problem for the case in which the clusters have to be disjoint and for the case where clusters can overlap. The analysis is often subtle and reveals interesting structure and invariants that one can utilize.

中文翻译：

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超图中的聚类以最小化平均边缘服务时间

我们研究了对加权超图的顶点进行聚类的问题，使得平均每条边的顶点可以被少量的聚类覆盖。这个问题有很多应用，例如设计医学测试，在磁盘服务器上集群文件，以及在服务器上放置网络服务。超图模型的边缘可能需要一起使用的项目组，我们使用的优化标准可以解释为为典型边缘的项目提供服务的平均延迟（或成本）。我们针对集群必须不相交和集群可以重叠的情况描述和分析该问题的算法。分析通常很微妙，并揭示了人们可以利用的有趣结构和不变量。