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The service placement problem is challenging due to the complexity of such distributed systems, limited computing resources, placement constraints, global efficiency of the application and quality requirements for end users. This survey attempts to provide a comprehensive and structured presentation of services placement problem research in integrated Cloud-Fog\/Edge. We propose a new classification of services placement problem approaches by adopting an algorithmic viewpoint and a breakdown into three categories: graph-based, heuristics and machine-learning approaches. We also provide an analysis and some discussions of the methods, and identify some future challenges and issues in the case of microservices. 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