— Ethernet over SONET (EoS) is a popular approach for interconnecting geographically distant Ethernet segments using a SONET transport infrastructure. It typically uses virtual concatenation (VC) for dynamic bandwidth management. The aggregate SONET bandwidth that supports a given EoS system is obtained by “concatenating” a number of virtual channels (VCs), which together form a virtually concatenated group (VCG). This aggregate bandwidth can be increased on demand by adding one or more VCs to the existing VCG. The new VC (route) must be selected such that its end-to-end delay is within a certain range that reflects the delays of all existing VCs in the VCG and the available memory buffer of the EoS system. Algorithmically, the problem of selecting such a VC becomes that of finding a path in a graph network that is bounded by an upper and lower bounds (the lower bound being a positive number). This problem, known as the two-sided constrained path (TSCP), was first formulated i...