Generalizing work of Künnemann, Paturi, and Schneider [ICALP 2017], we study a wide class of high-dimensional dynamic programming (DP) problems in which one must find the shortest path between two points in a high-dimensional grid given a tensor of transition costs between nodes in the grid. This captures many classical problems which are solved using DP such as the knapsack problem, the airplane refueling problem, and the minimal-weight polygon triangulation problem. We observe that for many of these problems, the tensor naturally has low tensor rank or low slice rank. We then give new algorithms and a web of fine-grained reductions to tightly determine the complexity of these problems. For instance, we show that a polynomial speedup over the DP algorithm is possible when the tensor rank is a constant or the slice rank is 1, but that such a speedup is impossible if the tensor rank is slightly super-constant (assuming SETH) or the slice rank is at least 3 (assuming the APSP conjecture). We find that this characterizes the known complexities for many of these problems, and in some cases leads to new faster algorithms.

Abstract Image outpainting aims at extending the field of view of an existing image. While image inpainting has achieved great success with the deep learning technology, image outpainting still receive less attention. The main challenge is how to generate high‐quality extended images with clear texture and highly consistent semantic information. In order to solve the problem of the effect of invalid pixels on the generated image and the distance of effective pixels is too far. This paper proposes a two‐stage image outpainting method (the EA method), which consists of an edge generation stage and an edge transformation stage. In this paper, the convolutional block attention module (CBAM) is introduced into the generation network to focus on spatial and channel feature and the improved VAE‐GAN structure is used to generate the extended image for more realistic semantics. The EA method is evaluated on the CelebA, Pairs‐streetview and homemade landscapes dataset, and show that the results contain high‐quality textures as well as faithfully extend the semantics. The average PSNR, SSIM, FID index of the EA method on the three datasets is 22.7961, 0.7061, 6.8553 and show that it outperforms existing algorithms in both quantitative and qualitative analysis.

To support the unrelenting demand of high spectral efficiency and gigabit data rates driven by fast developing smart applications and internet of things, heterogeneous cellular networks (HCNs) with the multiple-antenna configuration have been presented as promising paradigms. In this paper, the downlink transmission performances of K-tier HCNs with multiple-antenna configurations are analyzed, where base stations (BSs) in each tier may differ in terms of the spatial density, transmit power, cell-bias factor, and the number of transmit antennas. Particularly, the service success probability is analytically developed with the stochastic geometry, which can evaluate the transmission reliability and congestion. The impacts of the cell association and user scheduling on the service success probability are derived with closed-form expressions, and the spatial multiplexing gains from the multiple-antenna configuration are exploited. The Monte Carlo simulation results demonstrate that the derived expressions for the service success probability are matched well, and indicate that the proper number of antennas should be chosen, which is strictly related to the densities of BSs and users in each tier.

Future mobile wireless communication networks will be featured as heterogeneity in order to enhance network performance and improve user experience. For better adaption to network challenges over its complexity and vulnerability, cell outage detection technique, a promising intelligent part of self-organizing networks (SON), has drawn considerable attention to deal with unexpected network faults. Our work is devoted to cell outage detection in a two-tier macro-pico network. Based on observation of performance metrics in time domain, we employ a classification algorithm called K-nearest neighbor (KNN) to achieve automatic anomaly detection. With some reasonable assumptions and a LTE-A system simulator, numerical experiments are implemented to demonstrate the efficiency of the proposed algorithm. Finally, localization for anomaly data and performance evaluation are further carried out to validate the classification accuracy.