The p-center problem consists in selecting p facilities from a set of possible sites and allocating a set of clients to them in such a way that the maximum distance between a client and the facility to which it is allocated is minimized. This paper proposes a new scalable exact solution algorithm based on client clustering and an iterative distance rounding procedure. The client clustering enables to initialize and update a subset of clients for which the p-center problem is iteratively solved. The rounding drastically reduces the number of distinct distances considered at each iteration. Our algorithm is tested on 396 benchmark instances with up to 1.9 million clients and facilities. We outperform the two state-of-the-art exact methods considered when p is not very small (i.e., p > 5).

翻译：p-中心问题旨在从一组候选设施点中选取p个设施，并将客户集合分配给这些设施，使得客户与其分配设施之间的最大距离最小化。本文提出一种基于客户聚类与迭代距离舍入过程的新型可扩展精确求解算法。客户聚类技术能够初始化并动态更新一个客户子集，针对该子集迭代求解p-中心问题。距离舍入过程显著减少了每次迭代中需处理的相异距离数量。我们在包含最多190万个客户与设施的396个基准测试实例上验证了算法性能。当p值非极小（即p > 5）时，本算法优于当前两种最先进的精确求解方法。