An analysis between exact and approximate algorithms for the k-center problem in graphs

<span lang="EN-US">This research focuses on the k-center problem and its applications. Different methods for solving this problem are analyzed. The implementations of an exact algorithm and of an approximate algorithm are presented. The source code and the computation complexity of these algorithms are presented and analyzed. The multitasking mode of the operating system is taken into account considering the execution time of the algorithms. The results show that the approximate algorithm finds solutions that are not worse than two times optimal. In some case these solutions are very close to the optimal solutions, but this is true only for graphs with a smaller number of nodes. As the number of nodes in the graph increases (respectively the number of edges increases), the approximate solutions deviate from the optimal ones, but remain acceptable. These results give reason to conclude that for graphs with a small number of nodes the approximate algorithm finds comparable solutions with those founds by the exact algorithm.</span>

A Novel Sparse Array for Localization of Mixed Near-Field and Far-Field Sources

As we all know, nested array can obtain a larger array aperture and more degrees of freedom using fewer sensors. In this study, we not only designed an enhanced symmetric nested array (ESNA), which achieved more consecutive lags and more unique lags compared with a generalized nested array but also developed a special cumulant matrix, in the case of a given number of sensors, which can automatically generate the largest consecutive lags of the array. First, the direction-of-arrivals (DOAs) of mixed sources are estimated using the special cumulant matrix. Then, we can estimate the range of the near-field source in the mixed source using a one-dimensional spectral search through estimated DOAs, and in the mixed sources, the near-field and far-field sources are classified by bringing in the range parameter. The largest consecutive lags and composition method of ESNA are also given, under a given number of sensors.Our algorithm has moderate computation complexity, which provides a higher resolution and improves the parameters’ estimation accuracy. Numerical simulation results demonstrate that the proposed array showed an outstanding performance under estimation accuracy and resolution ability for both DOA and range estimation compared with existing arrays of the same physical array sensors.

Posture Detection of Individual Pigs Based on Lightweight Convolution Neural Networks and Efficient Channel-Wise Attention

In this paper, a lightweight channel-wise attention model is proposed for the real-time detection of five representative pig postures: standing, lying on the belly, lying on the side, sitting, and mounting. An optimized compressed block with symmetrical structure is proposed based on model structure and parameter statistics, and the efficient channel attention modules are considered as a channel-wise mechanism to improve the model architecture.The results show that the algorithm’s average precision in detecting standing, lying on the belly, lying on the side, sitting, and mounting is 97.7%, 95.2%, 95.7%, 87.5%, and 84.1%, respectively, and the speed of inference is around 63 ms (CPU = i7, RAM = 8G) per postures image. Compared with state-of-the-art models (ResNet50, Darknet53, CSPDarknet53, MobileNetV3-Large, and MobileNetV3-Small), the proposed model has fewer model parameters and lower computation complexity. The statistical results of the postures (with continuous 24 h monitoring) show that some pigs will eat in the early morning, and the peak of the pig’s feeding appears after the input of new feed, which reflects the health of the pig herd for farmers.

Asymptotically Effective Method to Explore Euler Path in a Graph

Euler path is one of the most interesting and widely discussed topics in graph theory. An Euler path (or Euler trail) is a path that visits every edge of a graph exactly once. Similarly, an Euler circuit (or Euler cycle) is an Euler trail that starts and ends on the same node of a graph. A graph having Euler path is called Euler graph. While tracing Euler graph, one may halt at arbitrary nodes while some of its edges left unvisited. In this paper, we have proposed some precautionary steps that should be considered in exploring a deadlock-free Euler path, i.e., without being halted at any node. Simulation results show that our proposed approach improves the process of exploring the Euler path in an undirected connected graph without interruption. Furthermore, our proposed algorithm is complete for all types of undirected Eulerian graphs. The paper concludes with the proofs of the correctness of proposed algorithm and its computation complexity.

Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables

High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs having the greatest membership degrees of 1. Firstly, by defining the medium of an RSTIT2-FV, its membership function, credibility distribution, and inverse distribution are analytically and explicitly expressed. Secondly, an operational law for fuzzy arithmetic operations regarding mutually independent RSTIT2-FVs is proposed, which can simplify the calculations and directly output the inverse credibility of the functions. Afterwards, the operational law is applied to define the expected value operator of the IT2-FV and prove the linearity of the operator. Finally, some comparative examples are provided to verify the efficiency of the proposed operational law.

A dynamic adaptive grating algorithm for AIS-based ship trajectory compression

Automatic identification system (AIS)-based ship trajectory data are important for analysing maritime activities. As the data accumulate over time, trajectory compression is needed to alleviate the pressure of data storage, migration and usage. The grating algorithm, as a vector data compression algorithm with high compression performance and low computation complexity, has been considered as a very promising approach for ship trajectory compression. This algorithm needs the threshold to be set for each trajectory which limits the applicability over a large number of different trajectories. To solve this problem, a dynamic adaptive threshold grating compression algorithm is developed. In this algorithm, the threshold for each trajectory is dynamically generated using an effective approaching strategy. The developed algorithm is tested with a complex trajectory dataset from the Qiongzhou Strait, China. In comparison with the traditional grating method, our algorithm has improved advantages in the ease of use, the applicability to different trajectories and compression performance, all of which can better support relevant applications, such as ship trajectory data storage and rapid cartographic display.

Maximum convergence algorithm for WiFi based indoor positioning system

WiFi-based indoor positioning is widely exploited thanks to the existing WiFi infrastructure in buildings and built-in sensors in smartphones. The techniques for indoor positioning require the high-density training data to archive high accuracy with high computation complexity. In this paper, the approach for indoor positioning systems which is called the maximum convergence algorithm is proposed to find the accurate location by the strongest receiver signal in the small cluster and K nearest neighbours (KNN) of other clusters. Also, the K-mean clustering is deployed for each access point to reduce the computation complexity of the offline databases. Moreover, the pedestrian dead reckoning (PDR) method and Kalman filter with the information from the received signal strength (RSS) and inertial sensors are applied to the WiFi fingerprinting to increase the efficiency of the mobile object's position. The different experiments are performed to compare the proposed algorithm with the others using KNN and PDR. The recommended framework demonstrates significant proceed based on the results. The average precision of this system can be lower than 1.02 meters when testing in the laboratory environment with an area of 7x7 m using three access points.

COMPUTATION COMPLEXITY OF DEEP RELU NEURAL NETWORKS IN HIGH-DIMENSIONAL APPROXIMATION

The purpose of the present paper is to study the computation complexity of deep ReLU neural networks to approximate functions in H\"older-Nikol'skii spaces of mixed smoothness $H_\infty^\alpha(\mathbb{I}^d)$ on the unit cube $\mathbb{I}^d:=[0,1]^d$. In this context, for any function $f\in H_\infty^\alpha(\mathbb{I}^d)$, we explicitly construct nonadaptive and adaptive deep ReLU neural networks having an output that approximates $f$ with a prescribed accuracy $\varepsilon$, and prove dimension-dependent bounds for the computation complexity of this approximation, characterized by the size and the depth of this deep ReLU neural network, explicitly in $d$ and $\varepsilon$. Our results show the advantage of the adaptive method of approximation by deep ReLU neural networks over nonadaptive one.

Tensor-Based Reduced-Dimension MUSIC Method for Parameter Estimation in Monostatic FDA-MIMO Radar

Frequency diverse array (FDA) radar has attracted much attention due to the angle and range dependence of the beam pattern. Multiple-input-multiple-output (MIMO) radar has high degrees of freedom (DOF) and spatial resolution. The FDA-MIMO radar, a hybrid of FDA and MIMO radar, can be used for target parameter estimation. This paper investigates a tensor-based reduced-dimension multiple signal classification (MUSIC) method, which is used for target parameter estimation in the FDA-MIMO radar. The existing subspace methods deteriorate quickly in performance with small samples and a low signal-to-noise ratio (SNR). To deal with the deterioration difficulty, the sparse estimation method is then proposed. However, the sparse algorithm has high computation complexity and poor stability, making it difficult to apply in practice. Therefore, we use tensor to capture the multi-dimensional structure of the received signal, which can optimize the effectiveness and stability of parameter estimation, reduce computation complexity and overcome performance degradation in small samples or low SNR simultaneously. In our work, we first obtain the tensor-based subspace by the high-order-singular value decomposition (HOSVD) and establish a two-dimensional spectrum function. Then the Lagrange multiplier method is applied to realize a one-dimensional spectrum function, estimate the direction of arrival (DOA) and reduce computation complexity. The transmitting steering vector is obtained by the partial derivative of the Lagrange function, and automatic pairing of target parameters is then realized. Finally, the range can be obtained by using the least square method to process the phase of transmitting steering vector. Method analysis and simulation results prove the superiority and reliability of the proposed method.