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Under the network function virtualization multi-domain orchestration approach, many service providers jointly manage the life cycle of network services composed of virtual network functions. Many orchestration algorithms have been published focusing on different tasks for the life cycle of network services. Nowadays, some general-purpose and architectural orchestration surveys have been published. However, currently, no survey classifies and evaluates distributed multi-domain orchestration algorithms. In this survey, we focus on multi-domain orchestration works from an algorithmic perspective by considering the cooperative and competitive approaches. Algorithms are classified and evaluated. We propose a taxonomy for works that consider different life cycle tasks of network services and evaluate them in the light of well-defined key requirements. This allows us to have a perspective on the current state of multi …