Abstract The orthogonal matching pursuit (OMP) algorithm is a classical greedy algorithm widely used in compressed sensing. The number of iterations required for the OMP algorithm to perform exact the recovery of sparse signals is a fundamental problem in signal processing. In this work, by investigating the relationship between the iteration number for OMP and the signal estimation error based on the restricted isometry property, the authors obtained tighter bounds on the number of iterations required to approximately recover a sparse signal with noise and exact support recovering for the noiseless cases of OMP.

Mobile-edge computing (MEC) sinks computation and storage capacities to network edge, where it is close to users to support delay-sensitive services. However, due to the dynamic and stochastic properties of MEC networks, the deployed services may be frequently migrated among edge servers to follow the mobility of users, which greatly increases the network operational cost. In this article, considering the service migration cost brought by user mobility, we study the joint optimization problem of service deployment and request routing decisions to maximize the long-term network utility of MEC networks. First, we propose a Lyapunov optimization-based online service migration algorithm to decompose the continuous optimization problem into a number of one-slot online optimization problems. Then, to address the NP-hard issue of one-slot optimization, we use a randomized rounding technique to implement service migration and request routing. Furthermore, through a closed-form theoretical analysis, we prove that the proposed algorithm not only greatly meets the local user requests and enables approximate performance guarantees but also adaptively balances the service migration cost and system performance online. Finally, extensive simulations are conducted, which demonstrate that our algorithm can efficiently utilize the storage and computation resources of edge servers, and maximize the long-term network utility while ensuring the stability of service migration cost.