In the problem called single resource constraint scheduling, we are given $m$ identical machines and a set of jobs, each needing one machine to be processed as well as a share of a limited renewable resource $R$. A schedule of these jobs is feasible if, at each point in the schedule, the number of machines and resources required by jobs processed at this time is not exceeded. It is NP-hard to approximate this problem with a ratio better than $3/2$. On the other hand, the best algorithm so far has an absolute approximation ratio of $2+\varepsilon$. This paper presents an algorithm with absolute approximation ratio~$(3/2+\varepsilon)$, which closes the gap between inapproximability and best algorithm except for a negligible small~$\varepsilon$.

翻译：在单一资源制约列表问题上,我们得到的是一美元相同的机器和一套工作,每套都需要一台机器处理,以及一定份额的可再生资源。如果在时间表的每个点上,不超过目前所处理的工作所需的机器和资源的数量,这些工作的时间表是可行的。很难用比重大于3/2美元来估计这个问题。另一方面,目前最好的算法的绝对近似率是2美元。本文提供了一种绝对近近似率~(3/2)美元算法,它缩小了目前所处理的机器和最佳算法之间的差距,只有微不足道的少量的1美元除外。