We propose and study the M^pUFLP (universal facility location problem in the p-th power of metric space) in this paper, where the universal facility location problem (UFLP) extends several classical facility location problems like the uncapacitated facility location, hard-capacitated facility location, soft-capacitated facility location, incremental-cost facility location, concave-cost facility location, etc. In UFLP, a set of facilities, a set of clients, as well as the distances between them are given. Each facility has its specific cost function w.r.t. the amount of clients assigned to that facility. The goal is to assign the clients to facilities such that the sum of facility cost and service cost is minimized. In traditional facility location problems, the unit service cost is proportional to the distance between the client and its assigned facility and thus metric. However, in our work, this assumption is removed and a generalized version of universal facility location problem is proposed, which is the so-called MⁿUFLP. When $p=2$, it is also known as $l_2^2$ measure considered by Jain and Vazirani [J. ACM'01] and Fernandes et al. [Math. Program.'15]. Particularly in this case, we extend their work to include the aforementioned variants of facility location and a local search based $(11.18+\epsilon )$-approximation algorithm is proposed. Furthermore, the reanalysis of the proposed algorithm gives a p-related performance guarantee for general p.

我们提出并研究将M ^p UFLP（在通用的工厂选址问题p在本文中，通用设施位置问题（UFLP）扩展了几个经典设施位置问题，例如无能力设施位置，硬能力设施位置，软能力设施位置，增量成本设施位置，在UFLP中，给出了一组设施，一组客户以及它们之间的距离。每个设施都有其特定的成本函数，其中包含分配给该设施的客户数量。目标是为客户分配设施，以使设施成本和服务成本之和最小。在传统的设施位置问题中，单位服务成本与客户与其分配的设施之间的距离成比例，因此也与度量成正比。但是，在我们的工作中^ñ UFLP。什么时候$p=2$，也称为 ${升}_2^2$Jain和Vazirani考虑的措施[J. ACM'01]和Fernandes等。[数学。程序。'15]。特别是在这种情况下，我们将他们的工作扩展到包括设施位置和基于本地搜索的上述变体$（11.18+\epsilon ）$提出了一种近似算法。此外，所提出算法的重新分析为一般p提供了与p相关的性能保证。