Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for makespan minimization on a fixed number of parallel machines, and other related variants. The running times of our algorithms are all of the form $\widetilde{O}(p^{O(1)}_{\max}+n)$ or $\widetilde{O}(p^{O(1)}_{\max} \cdot n)$, where $p_{\max}$ is the maximum processing time in the input. These improve upon the time complexity of previously known algorithms for moderate values of $p_{\max}$.

翻译：短整数线性规划是指约束数量相对较少的规划问题。本文展示了如何利用此类规划求解器在运行时间方面的最新改进，为固定数量并行机上的完工时间最小化及其相关变体问题设计快速的伪多项式时间算法。我们提出的算法运行时间均具有 $\widetilde{O}(p^{O(1)}_{\max}+n)$ 或 $\widetilde{O}(p^{O(1)}_{\max} \cdot n)$ 的形式，其中 $p_{\max}$ 表示输入中的最大处理时间。对于中等规模的 $p_{\max}$ 值，这些算法在时间复杂度上优于以往已知的算法。