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**1 - 1**of**1**### Flexible Resource Allocation for Optical Networks

"... Abstract. Motivated by flexible resource allocation in emerging net-work technologies, we study the following variant of the classic storage allocation problem. We are given a set of flexible axis-parallel rectangles (corresponding to activities), and a linear resource. Each rectangle has a maximum ..."

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Abstract. Motivated by flexible resource allocation in emerging net-work technologies, we study the following variant of the classic storage allocation problem. We are given a set of flexible axis-parallel rectangles (corresponding to activities), and a linear resource. Each rectangle has a maximum possible height, as well as the profit accrued per allocated unit of the resource. The goal is to feasibly allocate to each rectangle some amount of the resource (up to its maximum height), by sliding the rectangles vertically but not horizontally, such that the total profit is maximized. We first show that the flexible storage allocation problem (fsap) is strongly NP-hard already for highly restricted instances, where all of the rectan-gles have the same maximum height and the same (unit) profit, and ob-tain for this subclass the best possible result, namely, a polynomial time approximation scheme (PTAS). We then present a (5/4+ε)-approximation algorithm for general fsap instances where the input graph is proper (i.e., no activity is properly contained in another). Finally, we consider the flexible bandwidth allocation (fba) problem, in which the resource can be allocated in non-contiguous blocks, and the goal is to maximize resource utilization. By establishing an interesting relation to the paging problem, we show that fba can be optimally solved in linear time, even if each activity comes also with a minimum possible height. This substantially improves the running time of the best known algorithm for fba, based on flow techniques. Most of our algorithms are easy to implement, and are therefore practical.