E - An Algorithm for Minimum-Interference Routing in Linear Lightwave Networks

Summary

Given a source s and destination d for a point-to-point connection on a selected waveband in an LLN, the Min-Int algorithm presented here attempts to find a minimum-interference optical path p = 〈s, d〉 for that connection on the given waveband. The exact sense in which interference is minimized requires some explanation and is defined in Section E.3.

The Image Network

The approach used to find a path that minimizes interference is based on shortest path calculations, where the path “length” takes into account weights or “lengths” representing currently active interfering signals. These weights are associated with nodes rather than links. A useful way of visualizing the node-weighting procedure is shown in the image network of Figure E.1. In the network shown in the figure, each node of the original network is “blown up” to create additional intranodal links between each input/output port pair. This is nothing more than a representation of the internal structure of the LDC on the chosen waveband (see Figure 2.19[b]). The image network of Figure E.1 corresponds to the state of activity in the network of Figure 6.55. Two optical connections, (1, 1*) and (2, 2*), are active, with signal S₁ transmitted from station 1 to 1* and signal S₂ transmitted from station 2 to 2*.

We shall denote an internodal link from node i to node j by (i, j) and assign it a positive weight d(i, j).