Abstract
Completing possibly unforeseen tasks in a timely manner is vital for many real-world problems: For instance, in hospitals, emergency patients may come in and require to be treated, or self-driving cars need to avoid obstacles appearing on the street. Under the hard constraint of timely fulfilling these tasks, one still usually wishes to use resources conscientiously. We consider the above applications in the form of two fundamental mathematical problems. First, in online deadline scheduling, jobs arrive over time and need to scheduled on a machine until their deadline. Second, in convex-body chasing, an agent needs to immediately serve tasks located within convex regions and minimize the total travelled distance. In this paper we review the main results we obtained in the thesis of the same title: We present various novel online algorithms and techniques for analyzing them. Thereby we improve upon previously known bounds.
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Schewior, K. (2018). Handling Critical Jobs Online: Deadline Scheduling and Convex-Body Chasing. In: Kliewer, N., Ehmke, J., Borndörfer, R. (eds) Operations Research Proceedings 2017. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-89920-6_4
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DOI: https://doi.org/10.1007/978-3-319-89920-6_4
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