Brief Announcement: Flexible Resource Allocation for Clouds and All-Optical Networks

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, Ji, requires the use of up to rmax(i) units of the resource, with a profit of pi ≥ 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. We derive the best possible positive result for such instances, namely, a polynomial time approximation scheme (PTAS). We further show that the contiguous variant admits a (5/4+ε)-approximation algorithm, for any fixed ε >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. 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.