In the online facility assignment on a line (OFAL) with a set $S$ of $k$ servers and a capacity $c:S\to\mathbb{N}$, each server $s\in S$ with a capacity $c(s)$ is placed on a line and a request arrives on a line one-by-one. The task of an online algorithm is to irrevocably assign a current request to one of the servers with vacancies before the next request arrives. An algorithm can assign up to $c(s)$ requests to each server $s\in S$. In this paper, we show that the competitive ratio of the permutation algorithm is at least $k+1$ for OFAL where the servers are evenly placed on a line. This disproves the result that the permutation algorithm is $k$-competitive by Ahmed et al..

翻译：在线设施分配问题（OFAL）中，给定一组包含$k$个服务器的集合$S$及其容量函数$c:S\to\mathbb{N}$，每个服务器$s\in S$（容量为$c(s)$）位于一条直线上，请求按顺序逐个到达。在线算法的任务是在下一个请求到达前，不可撤销地将当前请求分配给有空位的服务器。每个服务器$s\in S$最多可分配$c(s)$个请求。本文证明，当服务器均匀分布在直线上时，排列算法的竞争比至少为$k+1$。这一结果否定了Ahmed等人关于排列算法具有$k$-竞争性的结论。