Abstract
We study online makespan scheduling with a fixed number of parallel machines. Jobs arrive in an online fashion in consecutive time steps, and must be scheduled both immediately and definitely. In contrast to the number of machines, the number of jobs is not known in advance. This paper focuses on the advice complexity of the problem. Basically, we ask how much additional information may help us to obtain solutions of high quality. Our main result is the construction of a (1 + ε)-competitive online algorithm with advice that reads a constant number of advice bits, for any ε > 0; here, “constant” means with respect to the input size, but our bound does depend on the number of machines and ε. This result is particularly interesting since it shows some very significant threshold behavior; it is known that, to be a little better, namely optimal, a linear number of advice bits is necessary. We also show that the advice can be derived from the input in polynomial time (with respect to the input size).
This work was partially supported by the SNF grant 200021-141089. A special case of the results presented in this work is a part of the author’s Bachelor’s thesis and was published as a technical report [8].
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Dohrau, J. (2015). Online Makespan Scheduling with Sublinear Advice. In: Italiano, G.F., Margaria-Steffen, T., Pokorný, J., Quisquater, JJ., Wattenhofer, R. (eds) SOFSEM 2015: Theory and Practice of Computer Science. SOFSEM 2015. Lecture Notes in Computer Science, vol 8939. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46078-8_15
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