A Simple Approach to Dynamic Optimisation of Flexible Optical Networks with Practical Application
Abstract
:1. Introduction and Background
2. Related Problems
- Instead, we require a dynamic, computationally-inexpensive solution to the problem, which can be implemented in real-time in response to changing traffic patterns.
3. Formulation of the Problem
DRP-FON: Minimise C(r) [objective function] s.t. m [constraint]
4. Related Algorithms
5. A Fast Heuristic Solution
AlgH (Calculate the hop matrix): ∀ ij, run DSPA to calculate H = (hij)
AlgV (Calculate the viability matrix): ∀ ij, set vij = T if (hij ≤ m) ∨ (∃ k … l, … s.t. (rk ∧ … ∧ rl = T) ∧ (hik ≤ m ∧ … ∧ hlj ≤ m)); vij = F otherwise
A certificate for DRP-FON can be verified in polynomial time by the following algorithm: run AlgH run AlgV if vij = T ∀ ij then certificate valid else certificate invalid
AlgR (Optimise the relay array): // DRP-FON-heuristic setrk = F ∀ k // All relays switched off run AlgH // Calculate hop lengths run AlgV // Calculate viable paths while ∃ ij s.t. vij = F do // if more relays needed { find k s.t. |{i: (vik = T) ∧ (ri = F)}| // Find relay that ≥ |{ i: (vij = T) ∧ (ri = F)}| ∀ j // … reaches most nodes setrk = T // Power this new relay run AlgV } // Recalculate viable paths
6. Testing and Evaluation
7. Extensions and Generalisations
GDRP-FON: Minimise C(r)[objective function] s.t. M, W [constraint]
AlgGV (calculate the viability matrix): ∀ij, setvij = Tif(hij ≤ mij) ∨ (∃k …l, … s.t. (pk ∧ … ∧ pl ∧ rk ∧ … ∧ rl = T) ∧ (hik ≤ mik ∧ … ∧ hlj ≤ mlj)); vij = Fotherwise
GDRP-FON is NP-hard since, for pk = T ∀k, dij = hij ∀ij and wij = mij = constant ∀ij, DRP-FON reduces to it. As before, a certificate for GDRP-FON can be verified in polynomial time by the following algorithm: run AlgGH run AlgGV if vij = T∀ij then certificate valid else certificate invalid Since GDRP-FON is NP-Hard and has polynomial time certificate verifiability, it is NP-complete.☐
AlgR (Optimise relay array): // GDRP-FON-heuristic setrk = F ∀k // All relays switched off run AlgGH // Calculate hop lengths run AlgGV // Calculate viable paths while ∃ij s.t. vij = F do // if more relays needed { find k s.t. |{i: (vik = T) ∧ (ri = F)}| // Find relay that ≥ |{ i: (vij = T) ∧ (ri = F)}| ∀j // … reaches the most nodes setrk = T // Power this new relay run AlgGV } // Recalculate viable paths
8. Conclusions and Future Work
- 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(n3) steps and O(n2) memory).
Conflicts of Interest
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Grout, V. A Simple Approach to Dynamic Optimisation of Flexible Optical Networks with Practical Application. Future Internet 2017, 9, 18. https://doi.org/10.3390/fi9020018
Grout V. A Simple Approach to Dynamic Optimisation of Flexible Optical Networks with Practical Application. Future Internet. 2017; 9(2):18. https://doi.org/10.3390/fi9020018
Chicago/Turabian StyleGrout, Vic. 2017. "A Simple Approach to Dynamic Optimisation of Flexible Optical Networks with Practical Application" Future Internet 9, no. 2: 18. https://doi.org/10.3390/fi9020018
APA StyleGrout, V. (2017). A Simple Approach to Dynamic Optimisation of Flexible Optical Networks with Practical Application. Future Internet, 9(2), 18. https://doi.org/10.3390/fi9020018