Online Minimum Makespan Scheduling with a Buffer

In this paper we study an online minimum makespan scheduling problem with a reordering buffer. We obtain the following results, which improve on work from FOCS 2008: i) for m identical machines, we give a 1.5-competitive online algorithm with a buffer of size 1.5m , which is better than the previous best result : 1.5-competitive algorithm with a buffer of size 1.6197m ; ii) for three identical machines, to give an optimal online algorithm we reduce the size of the buffer from nine to six; iii) for m uniform machines, using a buffer of size m , we improve the competitive ratio from 2+e to 2−1/m +e , where e >0 is sufficiently small.

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