Optimizing Bandwidth Allocation in Flex-Grid Optical Networks with Application to Scheduling

All-optical networks have been largely investigated due to their high data transmission rates. In the traditional Wavelength-Division Multiplexing (WDM) technology, the spectrum of light that can be transmitted through the optical fiber has been divided into frequency intervals of fixed width, with a gap of unused frequencies between them. Recently, an alternative emerging architecture was suggested which moves away from the rigid Dense WDM (DWDM) model towards a flexible model, where usable frequency intervals are of variable width (even within the same link). Each light path has to be assigned a frequency interval (sub-spectrum), which remains fixed through all of the links it traverses. Two different light paths using the same link must be assigned disjoint sub-spectra. This technology is termed flex-grid (or, flex-spectrum), as opposed to fixed-grid (or, fixed-spectrum) current technology. In this work we study a problem of optimal bandwidth allocation arising in the flex-grid technology. In this setting, each light path has a lower and upper bound on the width of its frequency interval, as well as an associated profit, and we want to find a bandwidth assignment that maximizes the total profit. This problem is known to be NP-Complete. We observe that, in fact, the problem is inapproximable within any constant ratio even on a path network. We further derive NP-hardness results and present approximation algorithms for several special cases of the path and ring networks, which are of practical interest. Finally, while in general our problem is hard to approximate, we show that an optimal solution can be obtained by allowing resource augmentation. Our study has applications also in real time scheduling.