The emerging 5G applications and the connectivity of billions of devices have driven the investigation of multi-domain heterogeneous converged optical networks. To support emerging applications with their diverse quality of service requirements, network slicing has been proposed as a promising technology. Network virtualization is an enabler for network slicing, where the physical network can be partitioned into different configurable slices in the multi-domain heterogeneous converged optical networks. An efficient resource allocation mechanism for multiple virtual networks in network virtualization is one of the main challenges referred as virtual network embedding (VNE). This paper is a survey on the state-of-the-art works for the VNE problem towards multi-domain heterogeneous converged optical networks, providing the discussion on future research issues and challenges. In this paper, we describe VNE in multi-domain heterogeneous converged optical networks with enabling network orchestration technologies and analyze the literature about VNE algorithms with various network considerations for each network domain. The basic VNE problem with various motivations and performance metrics for general scenarios is discussed. A VNE algorithm taxonomy is presented and discussed by classifying the major VNE algorithms into three categories according to existing literature. We analyze and compare the attributes of algorithms such as node and link embedding methods, objectives, and network architecture, which can give a selection or baseline for future work of VNE. Finally, we explore some broader perspectives in future research issues and challenges on 5G scenario, field trail deployment, and machine learning-based algorithms.
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