Abstract
We study a variant of online scheduling problems, the online realtime scheduling. It can be defined on a complete graph, where each node represents a communication agent, and a communication between two agents can be considered as an edge. An input is a sequence of communication jobs, each of which requires two specified agents to communicate during specified time period. Each agent can participate in at most one communication job. The task of an online algorithm is to schedule jobs so that the sum of the profits of completed communication jobs is maximized. In this paper, we improve the competitive ratio of the General Shelf based Max Matching (GSMM) algorithm from \(6 + 4 \sqrt{2} (\approx 11.66)\) to \(2 \sqrt{6} + 6 (\approx 10.90)\). We also prove that this ratio is optimal for GSMM. In addition, we study the case where each job has no slack time, namely, it must be either started immediately or rejected at its release time, and show the competitive ratio of GSMM is \(2 \sqrt{6} + 5 (\approx 9.90)\).
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Kobayashi, K., Okamoto, K. (2007). Improved Upper Bounds on the Competitive Ratio for Online Realtime Scheduling. In: Arge, L., Hoffmann, M., Welzl, E. (eds) Algorithms – ESA 2007. ESA 2007. Lecture Notes in Computer Science, vol 4698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75520-3_42
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DOI: https://doi.org/10.1007/978-3-540-75520-3_42
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