This paper provides an initial introduction to, and definition of, the 'Dynamically Powered Relays for a Flexible Optical Network' (DPR-FON) problem for opto-electro-optical (OEO) regenerators used in optical networks. In such networks, optical transmission parameters can be varied dynamically as traffic patterns change. This will provide different bandwidths, but also change the regeneration limits as a result. To support this flexibility, OEOs ('relays') may be switched on and off as

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... thus saving power. DPR-FON is shown to be NP-complete; consequently, solving such a dynamic problem in real-time requires a fast heuristic capable of delivering an acceptable approximation to the optimal configuration with low complexity. In this paper, just such an algorithm is developed, implemented, and evaluated against more computationally-demanding alternatives for two known cases. A number of real-world extensions are considered as the paper develops, combining to produce the 'Generalised Dynamically Powered Relays for a Flexible Optical Network' (GDPR-FON) problem. This, too, is analysed and an associated fast heuristic proposed, along with an exploration of the further research that is required. Future Internet 2017, 9, 18 2 of 11 shorter transmission limits and, thus, the need for more frequent regeneration and greater numbers of relays. The next section considers comparable optimisation problems, which yield some insight into the task at hand. Section 3 gives the initial formulation and complexity discussion. Useful related approaches are considered in Section 4, and these lead to the proposed algorithm in Section 5, which also provides the proof of NP-completeness. Section 6 tests the algorithm with two known library networks. In Section 7, the problem, and its solution, are generalised and the complexity considered once more. Section 8 suggests future work for other researchers. The paper's overall structure, switching as it does between definition and solution, may appear odd, but this approach is considerably shorter than dealing with each thread independently in turn. For the same reason, the notation is also slightly informal in places. Related Problems Some aspects of the efficient management [8] and optimisation [9] of FONs have been recently documented as the technology and its benefits have become more widely known. However, until now, the approach has been to define a multi-objective problem, involving several aspects of traffic management, in turn requiring expensive optimisation [10]. In [3], for example, a complex off-line linear programming formulation is given, which requires considerable computing power to solve. We propose two significant variations to this general approach in this paper: