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4.1. Model and Problem Definition
We consider the network model shown in Figure 1. The metro network has N nodes
where nodes 1, 2, …, N -1 are connected to N -1 respective local regions and node N is
connected to the wide area backbone network. In each local region, a node serves all the end
terminals in this region and grooms their traffic into one or more wavelength channels. The
nodes are connected to the multi-passive-combiner hub through optical fibers.
Figure 7. In this example, wavelength conflict is avoided because only the channels at distinct
wavelengths are connected to each passive combiner.
i d wavelength channels
The channel assignment problem is defined as follows: assign
from node i to node j within the metro hub for all 1, ij N
≤ ≤ (i.e., to fulfill the channel
requirements determined in Section 3), such that only the channels at distinct wavelengths are
connected to each passive combiner (i.e., to avoid wavelength conflict within the multi-
passive-combiner hub).
4.2. Channel Assignment Method
Our main idea for channel assignment is as follows. We first transform the channel
requirement matrix D to another representation such that the channel assignment problem
becomes a sequence of known combinatorial problems called distinct representatives
problems [26]. We solve the latter problems by applying the existing distinct representatives
algorithm, and then transform the resulting solutions to get the channel assignment.
Before explaining the details of channel assignment, we briefly review the concept of
distinct representatives [26]. Given the sets Ω , Ω , ⋅⋅⋅ , Ω , we select one item (called
representative ) from each set such that the selected representatives are different from each
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