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5G/6G services and applications, in the context of the eMBB, mMTC and uRLLC network slicing framework, whose network infrastructure requirements may span beyond the coverage area of a single Infrastructure Provider (InP), are envisaged to be supported by leasing resources from multiple InPs. A challenging aspect for a Service Provider (SP) is how to obtain an optimal set of InPs on which to provision the requests and the particular substrate nodes and links within each InP on which to map the different VNFs and virtual links of the service requests, respectively, for a seamless, reliable and cost-effective orchestration of service requests. Existing works in this area either perform service mapping in uncoordinated manner, do not incorporate service reliability or do so from the perspective of stateless VNFs. Also they assume full information disclosure, or are based on exact approaches, which considerations are not well suited for future network scenarios characterized by delay sensitive mission critical applications and resource constrained networks. This thesis contributes to the above challenge by breaking the multi-domain service orchestration problem into two interlinked sub-problems that are solved in a coordinated manner: (1) Request splitting/partitioning (sub-problem 1), involving obtaining a subset of InPs and the corresponding inter-domain links on which to provision the different VNFs and virtual links of the service request; (2) Intra-domain VNF orchestration (sub-problem 2), involving obtaining the intra-domain nodes and links to provision the VNFs and virtual links of the sub-SFC associated with each InP. In this way, the thesis …