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- W2408646906 abstract "Motivated by the cloud computing paradigm, and by key optimization problems in all-optical networks, we study two variants of the classic job interval scheduling problem, where a reusable resource is allocated to competing job intervals in a flexible manner. Each job, $J_i$, requires the use of up to $r_{max}(i)$ units of the resource, with a profit of $p_i geq 1$ accrued for each allocated unit. The goal is to feasibly schedule a subset of the jobs so as to maximize the total profit. The resource can be allocated either in contiguous or non-contiguous blocks. These problems can be viewed as flexible variants of the well known storage allocation and bandwidth allocation problems. We show that the contiguous version is strongly NP-hard, already for instances where all jobs have the same profit and the same maximum resource requirement. For such instances, we derive the best possible positive result, namely, a polynomial time approximation scheme. We further show that the contiguous variant admits a $(frac{5}{4} + varepsilon)$-approximation algorithm, for any fixed $varepsilon > 0$, on instances whose job intervals form a proper interval graph. At the heart of the algorithm lies a non-standard parameterization of the approximation ratio itself, which is of independent interest. For the non-contiguous case, we uncover an interesting relation to the paging problem that leads to a simple $O(n log n)$ algorithm for uniform profit instances of n jobs. The algorithm is easy to implement and is thus practical." @default.
- W2408646906 created "2016-06-24" @default.
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- W2408646906 date "2016-05-16" @default.
- W2408646906 modified "2023-10-14" @default.
- W2408646906 title "Flexible Resource Allocation for Clouds and All-Optical Networks." @default.
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