Abstract
We consider the semi-online multiprocessor scheduling problem with m identical, parallel machines to minimize the makespan, where the jobs arrive in decreasing order of processing times. The famous Longest Processing Time (LPT) algorithm by Graham (1966) [4] for the classical offline multiprocessor scheduling problem schedules the jobs in decreasing order of processing times and has a worst-case bound of 4/3−1/(3m). So far, no algorithm with a better competitive ratio than the LPT algorithm has been given for the semi-online scheduling problem with decreasing processing times. In this note, we present a 5/4-competitive algorithm for m≥3 and an algorithm that is the best possible for m=3, i.e. an algorithm with competitive ratio (1+37)/6.
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