Telecom carriers have announced new content services by making a partnership with content providers and offered popular video streaming to customers. Via the integration with edge networks, telecom carriers can procure various contents from content providers and place them on edge servers proximate to end users to serve real-time requests with high bandwidth and ultra-low latency. Nevertheless, it is challenging to consider the content procurement, placement, and services jointly due to the user preference, user distribution, storage capacity of edge server, economic costs, etc. Telecom carriers would like to balance the procuring, placing, and transfer costs. To address this problem, the paper formulates an optimization problem and then proposes an approximation algorithm. Finally, the simulation results manifest that our algorithm outperforms other baselines.

Dockless electric bike (E-bike) sharing has become a new urban modality of green transportation to offer convenient services. Typically, the service provider arranges a truck starting from the depot to visit multiple parking locations to replace low-energy batteries. However, visiting many parking locations may cause a considerable tour cost. One efficient way is to aggregate low-energy E-bikes together. Some incentive mechanisms are thus adopted to encourage E-bike users to move their bikes to suitable parking locations, but leading to an incentive cost. The service provider would like to balance the tour cost of the truck and the incentive cost of E-bike users. To address this problem, the paper formulates an optimization problem and then proposes an approximation algorithm. The simulation results with the real dataset show that our algorithm outperforms the other baselines.

An eigenmode-selection approach was recently presented for relay precoding subject to the minimum/maximum sum of condition numbers of the effective multiple-input multiple-output (MIMO) channels in a two-way amplify-and-forward (AF) MIMO relay system. Although this method can achieve close-to-optimal performance, it would involve high search complexity for the solution in a relay precoding set of size 2·M!, where M is the degrees of freedom of the MIMO relay system. In this paper, we propose low-complexity relay precoder designs based on eigenmode selection for two-way AF MIMO relay systems. We first exploit the properties of condition numbers of the effective MIMO channels, and then present two set-reduction methods accordingly for eigenmode-selection precoding to minimize/maximize the sum of condition numbers. As compared with the original eigenmode-selection precoding scheme, the proposed designs reach similar performance but reduce the search complexity by a factor of M(M-1).

In this paper, we present new relay precoder designs for two-way amplify-and-forward multiple-input multiple-output (MIMO) relay systems. We first derive the mean-squared error (MSE) matrices of the received signals at two terminals, and show that their behavior strongly depends on the singular values of the effective MIMO channels of the corresponding relay system. Motivated by this property, a set of relay precoders are constructed based on the singular vector subspaces of the MIMO channels, and one of them is selected for meeting a specific design criterion. Four design criteria are investigated, including the minimum sum of MSEs, the maximum sum of capacities, and the minimum or maximum sum of condition numbers, where the condition number is defined as the ratio of the largest to the smallest singular value of a MIMO channel. Compared to the conventional iterative methods, the proposed relay precoders based on minimizing the sum of MSEs or maximizing the sum of capacities achieve close performance while requiring much lower computational complexity. In contrast, the proposed designs based on minimizing or maximizing the sum of condition numbers provide further complexity reduction, with similar performance at high signal-to-noise ratios (SNRs) but a performance loss at low SNRs.