Makespan minimization for ordinal cardinality constrained scheduling

We consider ordinal scheduling on identical parallel machines with cardinality constraints. That is, a parameter k=1 is given such that no machine can contain more than k jobs. The objective is to assign the jobs to machines such that the makespan is minimized. In the ordinal setting, jobs are presented one by one and it is known that they arrive sorted by non-increasing sizes, but the specific sizes become known only after termination of the algorithm. An ordinal algorithm is compared to an optimal offline algorithm that knows all sizes, but it can also assign at most k jobs to each machine. Several simple algorithms achieve a competitive ratio of 2. In this work, we improve this ratio using a carefully designed algorithm.