It turns out that the frequency block scheduling problem also arises in a problem in modeling SONET ring networks. Steven Cosares of Dowling College presented his work on this applications.
Any network can be represented as a collection of rings. The bandwidth needed is a function of traffic capacity and connectivity.
There are two types of rings, unidirectional and bidirectional.
In unidirectional rings, the traffic is always flows in
the same direction.
Whenever a break occurs in the network, the direction is reversed.
For example, assume a-b-c-d is a ring.
Without loss of generality, we can assume that the
clockwise direction is always picked first,
making the ring of the following form:
.
Thus the path
would be used in order to communicate between a and d.
If one of the connections is broken, we alter the direction,
thus bipassing the broken link.
In this configuration one can view the total ring bandwidth as a series
of lanes, none of which can be shared.
The total bandwidth of the network
, where 
is the bandwidth required
for communication between i and j.
In a bidirectional ring, traffic can occur simultaneously in both directions. This will allow for a more efficient network, but the problem of assigning communication lanes to communication demand becomes more complex. One must choose not only the lane to a ssign to the communication, but the direction as well. This gives rise to a vertex coloring problem on circular arc-graph graph model. An approximate solution results from breaking the arc-graph into two interval graphs, each of which can be scheduled independently. This can be done by breaking the arc-graph at any node. All communication through that node will be considered as one interval graph, and all communication that did not go through the node will define the second interval graph.
This this problem is reduced to the previously discussed interval-packing problem. There are two simple approximation algorithms for this problem:
-
We slot the median of each gap on the x axis, recursively.
-
We approximate each block to have
height of 
for 
It seems reasonable to try to reduce this problem to the bin packing problem,
for which constant-factor approximation algorithms are known.
However, providing the approximation ratio of the first-fit decreasing
is complicated by the likely falsity
of the conjecture that for each block there exists an area below it
which is 
full, for some constant x.