On the Complexity of Computing Least Cost Disjoint Path Pair with Dependent Cost Structure in Optical Networks

In an optical wavelength division multiplexing (WDM) network establishing a survivable connection involves computation of least cost disjoint (working and protection) paths. In this work we study the problem of computing edge/node disjoint path pair in WDM networks with full wavelength converters for providing shared protection. To enable greater resource sharing among protection paths we introduce and formalize the concept of dependent cost structure of a protection path on its working path and the disjointedness of its working path with working paths of other existing connections. We prove that the problem of computing least cost disjoint paths with dependent cost structure is NP-complete. We also prove that it is hard to compute solutions with approximate guarantees.