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We propose an optimal scheme for finding end-to-end shortest disjoint paths with a given sequence of domains in path computation element-based multi-domain networks. We compute the shortest path over multiple domains in the forward direction and compute the disjoint path in the backward direction. The scheme has lower time and message complexity compared to contemporary schemes for finding optimal survivable paths across domains. We prove the optimality of the proposed scheme. To further simplify the implementations in practical scenarios, we also provide heuristic algorithms. Simulation results exhibit superior performance of the proposed optimal and heuristic algorithms compared to existing approaches.