Abstract
We consider the problem of scheduling a set of equal-length intervals arriving online, where each interval is associated with a weight and the objective is to maximize the total weight of completed intervals. An optimal 4-competitive algorithm has long been known in the deterministic case, but the randomized case remains open. We give the first randomized algorithm for this problem, achieving a competitive ratio of 3.618. We also prove a randomized lower bound of 4/3, which is an improvement over the previous 5/4 result, and a lower bound of 2 for a class of barely random algorithms which include our new algorithm. We also show that the techniques can be carried to the deterministic multiprocessor case, giving a 3.618-competitive 2-processor algorithm, a 5/4 lower bound for any number of processors, and a 2 lower bound for 2 processors.
The work described in this paper was fully supported by a grant from City University of Hong Kong (SRG 7001969), and NSFC Grant No. 70471035.
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Fung, S.P.Y., Poon, C.K., Zheng, F. (2007). Online Interval Scheduling: Randomized and Multiprocessor Cases . In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_19
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DOI: https://doi.org/10.1007/978-3-540-73545-8_19
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