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We explore the machine-minimizing job scheduling problem, which has a rich history in the line of research, under an online setting. We consider systems with arbitrary job arrival times, arbitrary job deadlines, and unit job execution time. For this problem, we present a lower bound 2.09 on the competitive factor of \emph{any} online algorithms, followed by designing a 5.2-competitive online algorithm. We also point out a false claim made in an existing paper of Shi and Ye regarding a further restricted case of the considered problem. To the best of our knowledge, what we present is the first concrete result concerning online machine-minimizing job scheduling with arbitrary job arrival times and deadlines.

Competitive Design and Analysis for Machine-Minimizing Job Scheduling Problem