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Design and analysis of constant competitive deterministic semi-onlinealgorithms for the multi-processor scheduling problem with small number ofidentical machines have gained significant research interest in the last twodecades. In the semi-online scheduling problem for makespan minimization, weare given a sequence of independent jobs one by one in order and upon arrival,each job must be allocated to a machine with prior knowledge of some ExtraPiece of Information (EPI) about the future jobs. Researchers have designedmultiple variants of semi-online scheduling algorithms with constantcompetitive ratios by considering one or more EPI. In this paper, we proposefour new variants of competitive deterministic semi-online algorithms forsmaller number of identical machines by considering two EPI such as Decr andSum. We obtain improved upper bound and lower bound results on the competitiveratio for our proposed algorithms, which are comparable to the best knownresults in the literature. In two identical machines setting with known Sum, weshow a tight bound of 1.33 on the competitive ratio by considering a sequenceof equal size jobs. In the same setting we achieve a lower bound of 1.04 and anupper bound of 1.16 by considering Sum and a sequence of jobs arriving in orderof decreasing sizes. For three identical machines setting with known Decr andSum, we show a lower bound of 1.11 on the competitive ratio. In this setting,we obtain an upper bound of 1.5 for scheduling a sequence of equal size jobsand achieves an upper bound of 1.2 by considering a sequence of decreasing sizejobs. Further we develop an improved competitive algorithm with an upper boundof 1.11 on the competitive ratio.

New Competitive Semi-online Scheduling Algorithms for Small Number of Identical Machines