Semi-online multiprocessor scheduling with the longest given processing time.

A semi-online multiprocessor scheduling problem with the longest given processing time is studied,and the objective is to minimize the makespan,i.e.the maximum completion time on the processors.It is shown that the lower bound of the problem is at least(33+3)/6 when the number of machine is greater than 6,and a semi-online algorithm is presented which has a competitive ratio at most 2-1/(m-1) for any number of processors.