We study ordinal makespan scheduling on small numbers of identical machines, with respect to two parallel solutions. In ordinal scheduling, it is known that jobs are sorted by non-increasing sizes, but the specific sizes are not known in advance. For problems with two parallel solutions, it is required to design two solutions, and the performance of algorithm is tested for each input using the best solution of the two. We find tight results for makespan minimization on two and three machines, and algorithms that have strictly better competitive ratios than the best possible algorithm with a single solution also for four and five machines. To prove upper bounds, we use a new approach of considering pairs of machines from the two solutions.

翻译：我们研究Ordinal 将空档时间排在少量的相同机器上, 涉及两个平行的解决方案。 在排列时, 人们知道工作是按不增加的大小来分类的, 但具体大小事先并不为人所知。 对于两个平行解决方案的问题, 需要设计两个解决方案, 并使用两种解决方案的最佳解决方案对每种输入进行算法的性能测试。 我们发现, 在两个和三台机器上, 以及比最佳的算法竞争率高得多的算法, 并且有四和五台机器的单一解决方案。 为了证明上限, 我们使用一种新的方法来考虑两种解决方案中的两对机器。