Optimal semi-online algorithms for machine covering

This paper investigates the semi-online machine covering problems on m≥3 parallel identical machines. Three different semi-online versions are studied and optimal algorithms are proposed. We prove that if the total processing time of all jobs or the largest processing time of all jobs is known in advance, the competitive ratios of the optimal algorithms are both m−1. If the total processing time and the largest processing time of all jobs are both known in advance, the competitive ratios of the optimal algorithms are when m=3, and m−2 when m≥4.