The establishment of inter-domain traffic engineered paths is a requisite to accomplishing an end-to-end bandwidth guarantee and end-to-end resource optimization. Though the inter-domain paths must be reliable, it is difficult to compute suitable backup inter-domain paths in advance when the traffic engineering information is not disclosed outside of each domain. This means that the inter-domain path computation must satisfy the severe requirement of path establishment delay, since all inter-domain paths traversing the links in failure need to be computed after the failure occurs. Though several inter-domain path computation schemes have been proposed, their relative characteristics remain unknown. First, this paper classifies the conventional inter-domain path computation schemes into two types, i.e. end-to-end and per-domain schemes, and compares their performances under various traffic loads. Based on results of the comparisons, this paper proposes an adaptive inter-domain path computation scheme that can satisfy the severe requirement of the path establishment delay. In this scheme, the domain sequence from the source node to the destination node is divided into multiple sub-domain sequences according to the traffic load in each domain. The end-to-end path computation scheme is applied to the sub-domain sequences under heavy traffic loads, while the per-domain path computation scheme is applied to those under normal traffic loads. The simulation results show that the proposed scheme can adaptively satisfy the requirement for the path establishment delay while it maintains the optimality of path computation, even if the traffic load applied to each domain changes.