# A Simple Approach to Dynamic Optimisation of Flexible Optical Networks with Practical Application
## 7 Extensions and Generalisations
|{\(i\): (\(v_{ik}\)=T)\(\land\) (\(r_{i}\)=F)}|//Findrelaythat \(\geq\)|{\(i\): (\(v_{ij}\)=T)\(\land\) (\(r_{i}\)=F)}|\(\forall j\)//...reachesthemostnodes set\(r_{k}\)=T//Powerthisnewrelay runAlgGV }//Recalculateviablepaths
```

As before, the GDRP-FON heuristic, AlgGR, can be considered an extension of the greedy 'ADD' algorithm in [16]. Again, it deals with the special case of an initial configuration (and values of \(M\) and \(W\)) requiring _no_ relays. Additionally, as before, AlgGR is polynomial by a similar argument. At this stage of the research, however, the AlgGR fast heuristic remains untested. Although AlgGR itself runs quickly, the brute force approach to finding the optimal comparison becomes intractable for GDRP-FON. A reliable branch-and-price-and-cut [22] or metaheuristic [21] will have to be developed. ## 8 Conclusions and Future Work

This concludes an introduction to the field. Taking into account recent advances in optical network technology, this work has introduced the newly-relevant DRP-FON relay management problem in its basic form, defined it formally, and proved its NP-completeness. A simple, fast heuristic, AlgR, has been presented and shown, by comparison with more computationally-expensive optimisation techniques, to give valid and reasonable results. Both the problem and fast solving heuristic have then been extended to a generalized case (GDRP-FON), also NP-complete, taking into account three real-world extensions. Finally, a generalized fast heuristic, AlgGR, has been proposed (but not tested). Future work should now expand the testing of AlgR and AlgGR with larger examples. Additionally, other researchers are invited to develop improved heuristics for the simple and generalised DRP-FON and GDRP-FON problems, always taking into account, however, the practical constraints of real-world implementation, namely:

* The algorithm may have to run, and frequently re-run, within the limited operating environment of production network equipment, implying that:
* The algorithm should be of polynomial complexity in both space and time (probably no worse than \(O(n^{3})\) steps and \(O(n^{2})\) memory). A final consideration is that, in some practical implementations, the algorithm may have to run in distributed, rather than centralised, form: i.e., independently--but cooperatively [27]--on each network device. This is non-trivial. **Conflicts of Interest:** The author declares no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results. ## References

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