A note on semi-online machine covering

In the machine cover problem we are given m machines and n jobs to be assigned (scheduled) so that the smallest load of a machine is as large as possible. A semi-online algorithm is given in advance the optimal value of the smallest load for the given instance, and then the jobs are scheduled one by one as they arrive, without any knowledge of the following jobs.We present a deterministic algorithm with competitive ratio 11/6 = 1.834 for machine covering with any number of machines and a lower bound showing that no deterministic algorithm can have a competitive ratio below 43/24 = 1.791