Flexible bandwidth assignment with application to optical networks

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.