1. A method of computing end-to-end paths through a network comprising a plurality of network domains, the method comprising the steps of: computing a first path segment within a first network domain using a child path computation element associated with the first network domain; computing a second path segment within a second network domain using a child path computation element associated with second the network domain; computing an end-to-end path across a plurality of network domains using a parent path computation element that computes the end-to-end path by joining the first path segment and the second path segment; generating, using the parent path computation element, a global identifier for the end-to-end path; communicating the global identifier from the parent path computation element to the child path computation element associated with the first network domain; generating, using the child path computation element associated with the first network domain, a local path identifier for the first path segment, the local path identifier comprising: the global identifier; an identifier for the first path segment; an identification of an ingress node of the first network domain; and an identification of an egress node of the first network domain, wherein the ingress node and the egress node are different nodes, the identifier for the first path segment is distinct from the identifications of the ingress and egress nodes; and communicating the local path identifier from the child path computation element associated with the first network domain to the ingress node of the first network domain.