约束容错资源分配
Constrained Fault-Tolerant Resource Allocation
摘要：
在约束容错资源分配（FTRA）问题中，我们给出了一组包含设施作为资源的站点，以及一组访问这些资源的客户端。具体地说，允许每个站点i最多开放R_i个设施，每个开放设施的成本为f_i。每个客户端j需要分配r_j个开放设施，将j连接到站点i的任何设施都会产生连接成本c_ij。目标是最小化此资源分配方案的总成本。FTRA推广了无约束容错资源分配（FTRA_{\infty}）[18]和经典容错设施定位（FTFL）[13]问题：对于每个站点i，FTRA_{\infty}没有约束R_i，而FTFL设置R_i=1。如果所有的r_j都相同，则这些问题称为一致问题，否则称为一般问题.对于一般的度量FTRA，我们首先给出了一个LP舍入算法，实现近似比为4。然后，我们证明问题归结为FTFL，这意味着[3]中的比率为1.7245。对于一致FTRA，我们提供了一个O（n^4）时间的1.52近似原始-对偶算法，其中n是站点和客户端的总数。我们还考虑了约束容错k-资源分配（k-FTRA）问题，其中可以在所有站点上打开的设施的总数由k限定。对于一致k-FTRA，我们给出了第一个常数因子近似算法，其因子为4。请注意，上述结果可推广到FTRA_{\infty}和k- FTRA_{\infty}。
英文摘要：
In the Constrained Fault-Tolerant Resource Allocation (FTRA) problem, we are given a set of sites containing facilities as resources, and a set of clients accessing these resources. Specifically, each site i is allowed to open at most R_i facilities with cost f_i for each opened facility. Each client j requires an allocation of r_j open facilities and connecting j to any facility at site i incurs a connection cost c_ij. The goal is to minimize the total cost of this resource allocation scenario. FTRA generalizes the Unconstrained Fault-Tolerant Resource Allocation (FTRA_{\infty}) [18] and the classical Fault-Tolerant Facility Location (FTFL) [13] problems: for every site i, FTRA_{\infty} does not have the constraint R_i, whereas FTFL sets R_i=1. These problems are said to be uniform if all r_j's are the same, and general otherwise. For the general metric FTRA, we first give an LP-rounding algorithm achieving the approximation ratio of 4. Then we show the problem reduces to FTFL, implying the ratio of 1.7245 from [3]. For the uniform FTRA, we provide a 1.52-approximation primal-dual algorithm in O(n^4) time, where n is the total number of sites and clients. We also consider the Constrained Fault-Tolerant k-Resource Allocation (k-FTRA) problem where additionally the total number of facilities can be opened across all sites is bounded by k. For the uniform k-FTRA, we give the first constant-factor approximation algorithm with a factor of 4. Note that the above results carry over to FTRA_{\infty} and k-FTRA_{\infty}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
