Abstract
This paper investigates online scheduling on m identical machines with splitting intervals, i.e., intervals can be split into pieces arbitrarily and processed simultaneously on different machines. The objective is to maximize the throughput, i.e., the total length of satisfied intervals. Intervals arrive over time and the knowledge of them becomes known upon their arrivals. The decision on splitting and assignment for each interval is made irrecoverably upon its arrival. We first show that any non-split online algorithms cannot have bounded competitive ratios if the ratio of longest to shortest interval length is unbounded. Our main result is giving an online algorithm ES (for Equivalent Split) which has competitive ratio of 2 and \(\frac{2m-1}{m-1}\) for m = 2 and m ≥ 3, respectively. We further present a lower bound of \(\frac{m}{m-1}\), implying that ES is optimal as m = 2.
This work was supported by NSF of China under Grants 70525004, 70702030, 70602031, and 60736027, and Doctoral Fund of Ministry of Education of China no. 20070698053.
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Zheng, F., Liu, B., Xu, Y., Zhang, E. (2010). Online Splitting Interval Scheduling on m Identical Machines. In: Chen, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2010. Lecture Notes in Computer Science, vol 6124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14355-7_31
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DOI: https://doi.org/10.1007/978-3-642-14355-7_31
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