Sequential metric dimension for random graphs

In the localization game on a graph, the goal is to find a fixed but unknown target node $v^\star$ with the least number of distance queries possible. In the jth step of the game, the player queries a single node $v_j$ and receives, as an answer to their query, the distance between the nodes $v_j$ and $v^\star$ . The sequential metric dimension (SMD) is the minimal number of queries that the player needs to guess the target with absolute certainty, no matter where the target is.The term SMD originates from the related notion of metric dimension (MD), which can be defined the same way as the SMD except that the player’s queries are non-adaptive. In this work we extend the results of Bollobás, Mitsche, and Prałat [4] on the MD of Erdős–Rényi graphs to the SMD. We find that, in connected Erdős–Rényi graphs, the MD and the SMD are a constant factor apart. For the lower bound we present a clean analysis by combining tools developed for the MD and a novel coupling argument. For the upper bound we show that a strategy that greedily minimizes the number of candidate targets in each step uses asymptotically optimal queries in Erdős–Rényi graphs. Connections with source localization, binary search on graphs, and the birthday problem are discussed.

Wireless Sensor Network Target Localization Algorithm Based on Two- and Three-Dimensional Delaunay Partitions

The target localization algorithm is critical in the field of wireless sensor networks (WSNs) and is widely used in many applications. In the conventional localization method, the location distribution of the anchor nodes is fixed and cannot be adjusted dynamically according to the deployment environment. The resulting localization accuracy is not high, and the localization algorithm is not applicable to three-dimensional (3D) conditions. Therefore, a Delaunay-triangulation-based WSN localization method, which can be adapted to two-dimensional (2D) and 3D conditions, was proposed. Based on the location of the target node, we searched for the triangle or tetrahedron surrounding the target node and designed the localization algorithm in stages to accurately calculate the coordinate value of the target. The relationship between the number of target nodes and the number of generated graphs was analysed through numerous experiments, and the proposed 2D localization algorithm was verified by extending it the 3D coordinate system. Experimental results revealed that the proposed algorithm can effectively improve the flexibility of the anchor node layout and target localization accuracy.

"Spectrally gapped" random walks on networks: a Mean First Passage Time formula

We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only input the transition probabilities into the target node. It is derived from the calculation of the average resolvent of a deformed ensemble of random sub-stochastic matrices H=\langle H\rangle +\delta HH=⟨H⟩+δH, with \langle H\rangle⟨H⟩ rank-11 and non-negative. The accuracy of the formula depends on the spectral gap of the reduced transition matrix, and it is tested numerically on several instances of (weighted) networks away from the high sparsity regime, with an excellent agreement.

Fundamental Limitations and State-of-the-art Solutions for Target Node Localization in WSNs

<p> </p><p>With the advances in new technological trends and the reduction in prices of sensor nodes, wireless sensor networks</p> <p>(WSNs) and their applications are proliferating in several areas of our society such as healthcare, industry, farming, and housing. Accordingly, in recent years attention on localization has increased significantly since it is one of the main facets in any WSN. In a nutshell, localization is the process in which the position of any sensor node is retrieved by exploiting measurements from and between sensor nodes. Several techniques of localization have been proposed in the literature with different localization accuracy, complexity, and hence different applicability. The localization accuracy is limited by fundamental limitations, theoretical and practical, that restrict the localization accuracy regardless of the technique employed in the localization process. In this paper, we pay special attention to such fundamental limitations from the theoretical and practical points of view and provide a comprehensive review of the state-of-the-art solutions that deal with such limitations. Additionally, discussion on the theoretical and practical limitations together with their recent solutions, remaining challenges, and perspectives are presented.</p> <p><br></p>

Fundamental Limitations and State-of-the-art Solutions for Target Node Localization in WSNs

<p> </p><p>With the advances in new technological trends and the reduction in prices of sensor nodes, wireless sensor networks</p> <p>(WSNs) and their applications are proliferating in several areas of our society such as healthcare, industry, farming, and housing. Accordingly, in recent years attention on localization has increased significantly since it is one of the main facets in any WSN. In a nutshell, localization is the process in which the position of any sensor node is retrieved by exploiting measurements from and between sensor nodes. Several techniques of localization have been proposed in the literature with different localization accuracy, complexity, and hence different applicability. The localization accuracy is limited by fundamental limitations, theoretical and practical, that restrict the localization accuracy regardless of the technique employed in the localization process. In this paper, we pay special attention to such fundamental limitations from the theoretical and practical points of view and provide a comprehensive review of the state-of-the-art solutions that deal with such limitations. Additionally, discussion on the theoretical and practical limitations together with their recent solutions, remaining challenges, and perspectives are presented.</p> <p><br></p>

Sequential Recommendation through Graph Neural Networks and Transformer Encoder with Degree Encoding

Predicting users’ next behavior through learning users’ preferences according to the users’ historical behaviors is known as sequential recommendation. In this task, learning sequence representation by modeling the pairwise relationship between items in the sequence to capture their long-range dependencies is crucial. In this paper, we propose a novel deep neural network named graph convolutional network transformer recommender (GCNTRec). GCNTRec is capable of learning effective item representation in a user’s historical behaviors sequence, which involves extracting the correlation between the target node and multi-layer neighbor nodes on the graphs constructed under the heterogeneous information networks in an end-to-end fashion through a graph convolutional network (GCN) with degree encoding, while the capturing long-range dependencies of items in a sequence through the transformer encoder model. Using this multi-dimensional vector representation, items related to the a user historical behavior sequence can be easily predicted. We empirically evaluated GCNTRec on multiple public datasets. The experimental results show that our approach can effectively predict subsequent relevant items and outperforms previous techniques.

An Approach of Extended Kalman Filter in Cooperative Localization

In this paper we explored the problem of localizing a mobile user within the range of a base station in 5G communication. For solving this problem we utilized Cooperative localization method over conventional localization technique to estimate the position of a mobile user. In cooperative localization we estimate position of the target user using Angle of Arrival(AOA), Time Difference of Arrival(TDOA) and Received Signal Strength(RSS) observations from nodes which are neighbour to target node and the base station. This estimation is done with the help of Extended Kalman Filter method.

Attack Prediction By Using Greedy Algorithm For Diminishing The Drop And Delay In Wireless Sensor Networks

The essential constraint of the internet is that forwarding the data packets of data among the restricted and trustworthy data nodes. If the receiver node is attacker node then it'll drop the data rather than forwarding the data to ensuing neighbor node. Therefore, efficient and secure data transmission is extremely necessary within the network data transmission. Each router node within the network can accept the data packets up to its buffer size only. Once the queue value reached the buffer threshold value then congestion can occur at the node. Once congestion happens then it would lose the data packets. By sending the data packets to the next neighbour node this problem will be resolved. This congestion will be handled by the Fully Distributed Congestion Control FDCC and Cooperative and Memory Efficient Token Bucket (CMTB) algorithms. Because the data is transmitted to the next neighbour node predicting the node behavior is extremely necessary because it is an attacker or the conventional transmitter node because it has to transmit the efficient data securely to the destination node. In this paper, the node behavior will be predicted by analyzing the trace file. The simulation results show that this proposed method would provide a lot of security in data transmission. The WSN comprises a group of sensor nodes that are disseminated on the network. These sensor nodes initially exchange their data packets to the near nodes to send the data packets to the target node. During the transmission of these data packets some data packets drop may also happen inside the network. This packet drop should be kept up as low as feasible for correct data transmission to the target node or destination node. This algorithm highlights the routes with high link quality, low packet delay and with low packet drop. Simulation results show that this proposed algorithm can provide the most effective path for transmitting the data to the destination meanwhile it reduces the packet drop and packet delay.

Fixed-Time Synchronization for Dynamical Complex Networks with Nonidentical Discontinuous Nodes

This article investigates the fixed-time synchronization issue for linearly coupled complex networks with discontinuous nonidentical nodes by employing state-feedback discontinuous controllers. Based on the fixed-time stability theorem and linear matrix inequality techniques, novel conditions are proposed for concerned complex networks, under which the fixed-time synchronization can be realized onto any target node by using a set of newly designed state-feedback discontinuous controllers. To some extent, this article extends and improves some existing results on the synchronization of complex networks. In the final numerical example section, the Chua circuit network is introduced to indicate the effectiveness of our method by showing its fixed-timely synchronization results with the proposed control scheme.

Chirp Spreading Spectrum in Imperfect Environment and Wireless Tree Topology Network

With the rapid development of IoT technology in recent years, higher requirements have been put forward for wireless communication technology. Low Power Wide Area Network (LPWAN) technology is emerging rapidly, the technology is characterized by low power consumption, low bandwidth, long-distance, and a large number of connections, and is specifically designed for Internet of Things applications. LoRa (Low Power Long Range Transceiver), as a typical representative of LPWAN technology, has been widely concerned and studied. This paper analyzes the performance of LoRa modulation in the tree topology network and analyzes the performance of LoRa modulation in the imperfect environment for point-to-point communication and multipoint-to-point communication. From theoretical analysis and performance simulation, it can be seen that the influence of frequency offset or multipath fading on LoRa signal is very obvious. However, when LoRa modulation is used for networking, multi-user interference will be introduced. Under the influence of many imperfect factors, the signal receiver performance of LoRa modulation will be difficult to guarantee. Because of these effects, Coordinated Multiple Points based on Timing Delay (DCoMP) is presented. Multiple nodes close to each other send the same data to the target node. Due to the inaccurate synchronization between nodes, there will be a certain relative delay when sending signals to the same target node. After the receiving node combines the signals of multiple nodes according to different relative delays, the reception performance of the signals can be improved. At the same time, the cooperative node can also actively adjust the signal sending time to improve the reception performance of the receiving node signal merging algorithm. LoRa modulation, by using DCoMP transmission, improves the reception of signals and thus the overall capacity of the system. Through the analysis of multipoint communication and single point communication, this paper is of great help to LoRa network deployment.