1. A method in a router for participating in computation of a constraint-based label switched path (LSP) that spans a plurality of areas to reach a destination, the router included within a first one of the plurality of areas, the method comprising the steps of: computing a path segment that meets a set of one or more constraints to at least one border router of the first area, wherein the at least one border router lies in a path necessary to reach the destination; transmitting a path computation request message to a path computation element in a second one of the plurality of areas, wherein the path computation request message includes a set of one or more attributes for each computed path segment that are used by the path computation element to compute one or more path segments towards the destination of the constraint-based LSP; receiving a path computation reply message from the path computation element that specifies a set of one or more computed path segments that meet the set of constraints and that were computed by one or more path computation elements downstream from the router; and stitching at least one of the set of computed path segments that are specified in the path computation reply message with the path segment computed by the router to form at least part of the constraint-based LSP.