Path Decomposition under a New Cost Measure
with Applications to Optical Network Design
Rensselaer Polytechnic Institute
Abstract. We introduce a problem directly inspired by its application to DWDM (dense wavelength
division multiplexing) network design. We are given a set of demands to be carried over a network.
Our goal is to choose a route for each demand and to decompose the network into a collection of
edge-disjoint simple paths. These paths are called optical line systems. The cost of routing one unit
of demand is the number of line systems with which the demand route overlaps; our design objective
is to minimize the total cost over all demands. This cost metric is motivated by the need to minimize
O-E-O (optical-electrical-optical) conversions in optical transmission.
For given line systems, it is easy to find the optimal demand routes. On the other hand, for given
demand routes designing the optimal line systems can be NP-hard. We first present a 2-approximation
that finds the optimal solution for the special case in which the node degree is at most 3. Our solution
is based on a local greedy approach.