In this paper, we study the problem of opening centers to cluster a set of clients in a metric space so as to minimize the sum of the costs of the centers and of the cluster radii, in a dynamic environment where clients arrive and depart, and the solution must be updated efficiently while remaining competitive with respect to the current optimal solution. We call this dynamic sum-of-radii clustering problem. We present a data structure that maintains a solution whose cost is within a constant factor of the cost of an optimal solution in metric spaces with bounded doubling dimension and whose worst-case update time is logarithmic in the parameters of the problem.

中文翻译：

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最小化半径总和的动态聚类

在本文中，我们研究了在客户到达和离开的动态环境中，开放中心以在度量空间中聚集一组客户的问题，以便最小化中心的成本和集群半径的总和，以及解决方案必须有效更新，同时保持相对于当前最佳解决方案的竞争力。我们称之为动态半径总和聚类问题。我们提出了一种数据结构，该结构维护一个解决方案，其成本在具有有界加倍维度的度量空间中最优解的成本的常数因子内，并且其最坏情况更新时间是问题参数的对数。