1. Effect of Maintaining Wavelength Continuity on Minimizing Network Coding Resources in Optical Long-haul Networks Ramanathan S Thinniyam

2. Approaches to Minimize Network Coding Resources 2-Stage approach 1. Minimize link cost (i.e. # of wavelengths) required to maintain given connection through Integer Programming to obtain subgraph. 2.Minimize coding cost (i.e. # of coded wavelengths) in subgraph obtained from stage 1 using a Genetic Algorithm(GA). Multi-Objective Evolutionary Approach(MOEA)- Obtain a Pareto front of tradeoffs between link cost and coding cost. Specifically, we use the NSGA –II algorithm * * K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II",IEEE Trans. Evol. Comput.,6(2):182–197(2002).

3. Wavelength Continuity Assume routing- dashed lines not routed, solid lines routed. In optical networks, O/E/O equipment can be used for both wavelength conversion as well to enable network coding. If case 2 uses O/E/O equipment at node 1 to maintain wavelength continuity, we can also code at this node if coding is allowed. 1 Case 1 1 Case 2

4. Simulation Results We perform experiments based on two different assumptions: 1.Hardware allowing wavelength conversion present at every node, cost of such conversion is zero (i.e. cost-free conversion). 2.O/E/O equipment present when conversion is needed (i.e. O/E/O based conversion). The cost of one or both coding and conversion at a node (or of a wavelength) is the same.

5. Results for O/E/O Based Continuity The fitness criterion is changed from number of coded wavelengths to number of wavelengths requiring O/E/O. # of wavelengths requiring O/E/O = # of solely converted wavelengths + # of coded wavelengths (coded wavelengths may or may not be converted). Results from 2 stage approach – never reduce O/E/O requirement to 0, – the number of O/E/O wavelengths on average is much higher than the number of coded wavelengths in cost-free conversion. – The cost of continuity is more O/E/O equipment

6. Fraction of nodes where O/E/O equipment is required is much larger than fraction of wavelengths, when optimizing using number of wavelengths as criterion. 2-Stage Approach Result 1- Average Network Coding Requirement

7. Conversion fraction=(Number of converted wavelengths)/(number of O/E/O wavelengths) Most problem instances show low conversion fraction < 1/3 2-Stage Approach Result 2 - Coding vs Conversion

8. 2-Stage Approach Result 3 -Distribution of Number of O/E/O Wavelengths

10. 2-Stage Approach Result 4a- Comparing Cost-free vs O/E/O

11. 2-Stage Approach Result 4b - Comparing Cost-free vs O/E/O

12. 2-Stage Approach Result 5- High Frequency Nodes ARPANET NSFNET NJLATA Nodes which were O/E/O nodes in the solution obtained in more than half the problem instances indicated in red.