Abstract
The concept of competitive-ratio approximation scheme was recently proposed in [7]. Such a scheme algorithmically constructs an online algorithm with a competitive ratio arbitrarily close to the best possible competitive ratio for a given online problem. In this paper we continue this line of research by addressing several makespan scheduling problems and introducing new ideas: we combine the classical technique of structuring and simplifying the input instance for approximation schemes, with the new technique of guessing the end of the schedule (time after which no job is processed and released), which allows us to reduce the infinite-size set of on-line algorithms to a relevant set of finite size. This is the key idea for eventually allowing an enumeration scheme that finds a near optimal on-line algorithm. We demonstrate how this technique can be successfully applied to three basic makespan online over time scheduling problems: scheduling on unrelated parallel machines, job shop scheduling and single machine scheduling with delivery times.
Supported by the Swiss National Science Foundation Project N.200020-122110/1 “Approximation Algorithms for Machine Scheduling Through Theory and Experiments III” and by Hasler Foundation Grant 11099.
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Kurpisz, A., Mastrolilli, M., Stamoulis, G. (2013). Competitive-Ratio Approximation Schemes for Makespan Scheduling Problems. In: Erlebach, T., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2012. Lecture Notes in Computer Science, vol 7846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38016-7_14
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DOI: https://doi.org/10.1007/978-3-642-38016-7_14
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