Abstract
We introduce two scheduling problems, the flexible bandwidth allocation problem (\(\textsc {FBAP}\)) and the flexible storage allocation problem (\(\textsc {FSAP}\)). In both problems, we have an available resource, and a set of requests, each consists of a minimum and a maximum resource requirement, for the duration of its execution, as well as a profit accrued per allocated unit of the resource. In \(\textsc {FBAP}\), the goal is to assign the available resource to a feasible subset of requests, such that the total profit is maximized, while in \(\textsc {FSAP}\) we also require that each satisfied request is given a contiguous portion of the resource. Our problems generalize the classic bandwidth allocation problem (BAP) and storage allocation problem (SAP) and are therefore \(\text {NP-hard}\). Our main results are a 3-approximation algorithm for \(\textsc {FBAP}\) and a \((3+\epsilon )\)-approximation algorithm for \(\textsc {FSAP}\), for any fixed \(\epsilon >0 \). These algorithms make nonstandard use of the local ratio technique. Furthermore, we present a \((2+\epsilon )\)-approximation algorithm for \(\textsc {SAP}\), for any fixed \(\epsilon >0 \), thus improving the best known ratio of \(\frac{2e-1}{e-1} + \epsilon \). Our study is motivated also by critical resource allocation problems arising in all-optical networks.
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We note that our results can be adapted also to instances when a(I), b(I) and w(I) are non-integers.
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We thank Dror Rawitz for valuable discussions.
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A preliminary version of this paper appeared in the proceedings of the \(39\mathrm {th}\) International Symposium on Mathematical Foundations of Computer Science(MFCS), 2014.
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Shachnai, H., Voloshin, A. & Zaks, S. Flexible bandwidth assignment with application to optical networks. J Sched 21, 327–336 (2018). https://doi.org/10.1007/s10951-017-0514-4
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DOI: https://doi.org/10.1007/s10951-017-0514-4