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Dubbed "the successor to the mobile Internet", the concept of the Metaverse has grown in popularity. While there exist lite versions of the Metaverse today, they are still far from realizing the full vision of an immersive, embodied, and interoperable Metaverse. Without addressing the issues of implementation from the communication and networking, as well as computation perspectives, the Metaverse is difficult to succeed the Internet, especially in terms of its accessibility to billions of users today. In this survey, we focus on the edge-enabled Metaverse to realize its ultimate vision. We first provide readers with a succinct tutorial of the Metaverse, an introduction to the architecture, as well as current developments. To enable the ubiquitous, seamless, and embodied access to the Metaverse, we discuss the communication and networking challenges and survey cutting-edge solutions and concepts that leverage next-generation communication systems for users to be telepresent and teleoperate in the Metaverse. Moreover, given the high computation costs required, e.g., to render immersive 3D worlds and run data hungry artificial intelligence (AI) driven applications, we discuss the computation challenges and cloud-edge-end computation framework driven solutions to realize the Metaverse on resource-constrained edge devices. Next, we explore how blockchain technologies can aid in the interoperable development of the Metaverse, not just in terms of empowering the economic circulation of virtual usergenerated contents, but also to manage physical edge resources in a decentralized, transparent, and tamper-proof manner. Finally, we discuss the future research directions towards realizing the true vision of the edge-enabled Metaverse.

Dubbed as the next-generation Internet, the metaverse is a virtual world that allows users to interact with each other or objects in real-time using their avatars. The metaverse is envisioned to support novel ecosystems of service provision in an immersive environment brought about by an intersection of the virtual and physical worlds. The native AI systems in metaverse will personalized user experience over time and shape the experience in a scalable, seamless, and synchronous way. However, the metaverse is characterized by diverse resource types amid a highly dynamic demand environment. In this paper, we propose the case study of virtual education in the metaverse and address the unified resource allocation problem amid stochastic user demand. We propose a stochastic optimal resource allocation scheme (SORAS) based on stochastic integer programming with the objective of minimizing the cost of the virtual service provider. The simulation results show that SORAS can minimize the cost of the virtual service provider while accounting for the users' demands uncertainty.

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Unmanned aerial vehicles (UAVs) have gained wide research interests due to their technological advancement and high mobility. The UAVs are equipped with increasingly advanced capabilities to run computationally intensive applications enabled by machine learning techniques. However, because of both energy and computation constraints, the UAVs face issues hovering in the sky while performing computation due to weather uncertainty. To overcome the computation constraints, the UAVs can partially or fully offload their computation tasks to the edge servers. In ordinary computation offloading operations, the UAVs can retrieve the result from the returned output. Nevertheless, if the UAVs are unable to retrieve the entire result from the edge servers, i.e., straggling edge servers, this operation will fail. In this paper, we propose a coded distributed computing approach for computation offloading to mitigate straggling edge servers. The UAVs can retrieve the returned result when the number of returned copies is greater than or equal to the recovery threshold. There is a shortfall if the returned copies are less than the recovery threshold. To minimize the cost of the network, energy consumption by the UAVs, and prevent over and under subscription of the resources, we devise a two-phase Stochastic Coded Offloading Scheme (SCOS). In the first phase, the appropriate UAVs are allocated to the charging stations amid weather uncertainty. In the second phase, we use the z-stage Stochastic Integer Programming (SIP) to optimize the number of computation subtasks offloaded and computed locally, while taking into account the computation shortfall and demand uncertainty. By using a real dataset, the simulation results show that our proposed scheme is fully dynamic, and minimizes the cost of the network and UAV energy consumption amid stochastic uncertainties.