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Emerging applications with low-latency requirements such as real-time analytics, immersive media applications, and intelligent virtual assistants have rendered Edge Computing as a critical computing infrastructure. Existing studies have explored the cloudlet placement problem in a homogeneous scenario with different goals such as latency minimization, load balancing, energy efficiency, and placement cost minimization. However, placing cloudlets in a highly heterogeneous deployment scenario considering the next-generation 5G networks and IoT applications is still an open challenge. The novel requirements of these applications indicate that there is still a gap in ensuring low-latency service guarantees when deploying cloudlets. Furthermore, deploying cloudlets in a cost-effective manner and ensuring full coverage for all users in edge computing are other critical conflicting issues. In this article, we address these issues by designing a bifactor approximation algorithm to solve the heterogeneous cloudlet placement problem to guarantee a bounded latency and placement cost, while fully mapping user applications to appropriate cloudlets. We first formulate the problem as a multi-objective integer programming model and show that it is a computationally NP-hard problem. We then propose a bifactor approximation algorithm, ACP, to tackle its intractability. We investigate the effectiveness of ACP by performing extensive theoretical analysis and experiments on multiple deployment scenarios based on New York City OpenData. We prove that ACP provides a (2,4)-approximation ratio for the latency and the placement cost. The experimental results show that ACP obtains near-optimal results in a polynomial running time making it suitable for both short-term and long-term cloudlet placement in heterogeneous deployment scenarios. [ABSTRACT FROM AUTHOR]

This paper studies a general framework for high-order tensor SVD. We propose a new computationally efficient algorithm, tensor-train orthogonal iteration (TTOI), that aims to estimate the low tensor-train rank structure from the noisy high-order tensor observation. The proposed TTOI consists of initialization via TT-SVD [Oseledets (2011)] and new iterative backward/forward updates. We develop the general upper bound on estimation error for TTOI with the support of several new representation lemmas on tensor matricizations. By developing a matching information-theoretic lower bound, we also prove that TTOI achieves the minimax optimality under the spiked tensor model. The merits of the proposed TTOI are illustrated through applications to estimation and dimension reduction of high-order Markov processes, numerical studies, and a real data example on New York City taxi travel records. The software of the proposed algorithm is available online (https://github.com/Lili-Zheng-stat/TTOI). [ABSTRACT FROM AUTHOR]