Pair Of Nodes Research Articles

A Simple and Efficient Method for Accelerating Construction of the Gap-Greedy Spanner

Let [Formula: see text] be the complete Euclidean graph on a set of points embedded in the plane. Given a constant [Formula: see text], a spanning subgraph [Formula: see text] of [Formula: see text] is said to be a [Formula: see text]-spanner, or simply a spanner, if for any pair of nodes [Formula: see text], [Formula: see text] in [Formula: see text] there exists a [Formula: see text]-path in [Formula: see text], i.e., a path between [Formula: see text] and [Formula: see text] whose length is at most [Formula: see text] times their distance in [Formula: see text]. Gap-greedy spanner, proposed by Arya and Smid, is a light weight and bounded degree spanner in which a pair of points [Formula: see text] is guaranteed to have a [Formula: see text]-path, if there exists at least one edge with some special criteria in the spanner. Existing algorithms for computing the gap-greedy spanner determine the existence of such an edge for each pair of points by examining the edges of the spanner, which takes [Formula: see text] time, however in this paper, we have presented a method by which this task can be done in [Formula: see text] time. Using the proposed method and well-separated pair decomposition, we have proposed a linear-space algorithm that can compute the gap-greedy spanner in [Formula: see text] time. How to use the well-separated pair decomposition to compute this spanner was proposed by Bakhshesh and Farshi, however using an example, we have shown that one of the algorithms they have proposed for this purpose is incorrect. We have performed various experiments to measure the duration and amount of memory used by the algorithms for computing this spanner. The results of these experiments showed that the proposed method, without a significant effect on the amount of memory consumed compared to previous algorithms, leads to a significant acceleration in the construction time of this spanner.

Recursive State Machine Guided Graph Folding for Context-Free Language Reachability

Context-free language reachability (CFL-reachability) is a fundamental framework for program analysis. A large variety of static analyses can be formulated as CFL-reachability problems, which determines whether specific source-sink pairs in an edge-labeled graph are connected by a reachable path, i.e., a path whose edge labels form a string accepted by the given CFL. Computing CFL-reachability is expensive. The fastest algorithm exhibits a slightly subcubic time complexity with respect to the input graph size. Improving the scalability of CFL-reachability is of practical interest, but reducing the time complexity is inherently difficult. In this paper, we focus on improving the scalability of CFL-reachability from a more practical perspective---reducing the input graph size. Our idea arises from the existence of trivial edges, i.e., edges that do not affect any reachable path in CFL-reachability. We observe that two nodes joined by trivial edges can be folded---by merging the two nodes with all the edges joining them removed---without affecting the CFL-reachability result. By studying the characteristic of the recursive state machines (RSMs), an alternative form of CFLs, we propose an approach to identify foldable node pairs without the need to verify the underlying reachable paths (which is equivalent to solving the CFL-reachability problem). In particular, given a CFL-reachability problem instance with an input graph G and an RSM, based on the correspondence between paths in G and state transitions in RSM, we propose a graph folding principle, which can determine whether two adjacent nodes are foldable by examining only their incoming and outgoing edges. On top of the graph folding principle, we propose an efficient graph folding algorithm GF. The time complexity of GF is linear with respect to the number of nodes in the input graph. Our evaluations on two clients (alias analysis and value-flow analysis) show that GF significantly accelerates RSM/CFL-reachability by reducing the input graph size. On average, for value-flow analysis, GF reduces 60.96% of nodes and 42.67% of edges of the input graphs, obtaining a speedup of 4.65× and a memory usage reduction of 57.35%. For alias analysis, GF reduces 38.93% of nodes and 35.61% of edges of the input graphs, obtaining a speedup of 3.21× and a memory usage reduction of 65.19%.

Super Spanning Connectivity of the Folded Divide-and-SwapCube

A k*-container of a graph G is a set of k disjoint paths between any pair of nodes whose union covers all nodes of G. The spanning connectivity of G, κ*(G), is the largest k, such that there exists a j*-container between any pair of nodes of G for all 1≤j≤k. If κ*(G)=κ(G), then G is super spanning connected. Spanning connectivity is an important property to measure the fault tolerance of an interconnection network. The divide-and-swap cube DSCn is a newly proposed hypercube variant, which reduces the network cost from O(n2) to O(nlog2n) compared with the hypercube and other hypercube variants. The folded divide-and-swap cube FDSCn is proposed based on DSCn to reduce the diameter of DSCn. Both DSCn and FDSCn possess many better properties than hypercubes. In this paper, we investigate the super spanning connectivity of FDSCn where n=2d and d≥1. We show that κ*(FDSCn)=κ(FDSCn)=d+2, which means there exists an m-DPC(node-disjoint path cover) between any pair of nodes in FDSCn for all 1≤m≤d+2.

Optimization of Mobile Robotic Relay Operation for Minimal Average Wait Time

This paper considers trajectory planning for a mobile robot which persistently relays data between pairs of far-away communication nodes. Data accumulates stochastically at each source, and the robot must move to appropriate positions to enable data offload to the corresponding destination. The robot needs to minimize the average time that data waits at a source before being serviced. We are interested in finding optimal robotic routing policies consisting of 1) locations where the robot stops to relay (relay positions) and 2) conditional transition probabilities that determine the sequence in which the pairs are serviced. We first pose this problem as a non-convex problem that optimizes over both relay positions and transition probabilities. To find approximate solutions, we propose a novel algorithm which alternately optimizes relay positions and transition probabilities. For the former, we find efficient convex partitions of the non-convex relay regions, then formulate a mixed-integer second-order cone problem. For the latter, we find optimal transition probabilities via sequential least squares programming. We extensively analyze the proposed approach and mathematically characterize important system properties related to the robot’s long-term energy consumption and service rate. Finally, through extensive simulation with real channel parameters, we verify the efficacy of our approach.

Gene expression comparison between primary aggressive luminal breast cancer and paired axillary and sentinel lymph node metastasis.

e13060 Background: More aggressive and therapy-resistant hormone receptor (HR)-positive breast cancer (hereafter luminal breast cancer, LBC) remains a great challenge. Few studies examine the genomics of axillary lymph node (ALN) metastasis in LBC. The aim of this study was to characterize and compare the mRNA expression patterns of primary breast cancers and paired ALN metastases. Methods: Aggressive pT1-2N2-3M0 LBC patients aged over 18 years who were treated at Shandong Provincial Hospital Affiliated to Shandong First Medical University and had available matched primary and metastatic tumor samples for gene expression analyses were retrospectively recruited. Bulk mRNA expression levels were determined by RNA sequencing (Illumina NovaSeq 6000 system) and calculated using featureCounts. Differential gene expression analysis was performed using DESeq2. All analyses were carried out with differentially expressed genes (DEGs) with an FDR <0.05. Changes of intrinsic subtypes from primary to metastatic disease were assessed. Results: Ten LBC patients with paired tumor samples were included. Compared with the primary tumor, ALN metastatic tumor had 1509 statistically significant DEGs, including 743 upregulated genes and 766 downregulated genes. Notably, there was an upregulation of genes related to immune response-activating signal transduction, T cell receptor signaling pathway, B cell receptor signaling pathway, and cytokine-cytokine receptor interaction in the ALN metastasis. The downregulation of genes were mainly enriched in the PI3K-Akt signaling pathway, ECM-receptor interaction, Wnt signaling pathway, and TGF-beta signaling pathway. Intrinsic subtype distribution in primary tumors was different from those in ALN metastatic tumors, such as Luminal A (30% vs. 50%), Luminal B (10% vs. 20%), HER2-enriched (20% vs. 10%), Basal-like (10% vs. 10%), and Normal-like (30% vs. 10%). These results suggest that LBC is a highly heterogeneous disease. Conclusions: In aggressive pT1-2N2-3M0 LBC, ALN metastases have a distinct gene expression profile and show upregulation of immune-related genes ( CR2, BLK, PAX5, CD19, FCRL1, TNFRSF13B). Genes associated with signaling pathways are involved in the development of breast cancer ( FST, TNN, LAMC3, SFRP2, FGF18), and are downregulated when compared to autologous primary cancer. These pathways are potential targeted pathways in the treatment of breast cancer. LBC cells metastatic to lymph nodes undergo a change to metastasize and survive in the new microenvironment, which may provide insights into the metastatic process. Besides, a switch towards more aggressive intrinsic subtype from primary to advanced disease is also observed.

Percolation in fractal spatial networks with long-range interactions

We study the emergence of a giant component in a spatial network where the nodes form a fractal set, and the interaction between the nodes has a long-range power-law behavior. The nodes are positioned in the metric space using a L\`evy flight procedure, with an associated scale-invariant step probability density function, that is then followed by a process of connecting each pair of nodes with a probability that depends on the distance between them. Since the nodes are positioned sequentially, we are able to calculate the probability for an edge between any two nodes in terms of their indexes and to map the model to the problem of percolation in a one-dimensional lattice with long-range interactions. This allows the identification of the conditions for which a percolation transition is possible. The system is characterized by two control parameters which determine the fractal dimension of the nodes and the power law decrease of the probability of a bond with the distance between the nodes. The competition between these two parameters forms an intricate phase diagram, which describes when the system has a stable giant component, and when percolation transitions occur. Understanding the structure of this class of spatial networks is important when analyzing real systems, which are frequently heterogeneous and include long-range interactions.

Efficient Resistance Distance Computation: The Power of Landmark-based Approaches

Resistance distance is a fundamental metric to measure the similarity between two nodes in graphs which has been widely used in many real-world applications. In this paper, we study two problems on approximately computing resistance distance: (i) single-pair query which aims at calculating the resistance distance r(s, t) for a given pair of nodes (s, t); and (ii) single-source query which is to compute all the resistance distances r(s, u) for all nodes u in the graph with a given source node s. Existing algorithms for these two resistance distance query problems are often costly on large graphs. To efficiently solve these problems, we first establish several interesting connections among resistance distance, a new concept called v-absorbed random walk, random spanning forests, and a newly-developed v-absorbed push procedure. Based on such new connections, we propose three novel and efficient sampling-based algorithms as well as a deterministic algorithm for single-pair query; and we develop an online and two index-based approximation algorithms for single-source query. We show that the two index-based algorithms for single-source query take almost the same running time as the algorithms for single-pair query with the aid of a linear-size index. The striking feature of all our algorithms is that they are allowed to select an easy-to-hit node by random walks on the graph. Such an easy-to-hit landmark node v can make the v-absorbed random walk sampling, spanning tree sampling, as well as the v-absorbed push more efficient, thus significantly improving the performance of our algorithms. Extensive experiments on 5 real-life datasets show that our algorithms substantially outperform the state-of-the-art algorithms for two resistance distance query problems in terms of both running time and estimation errors.

Efficient Estimation of Pairwise Effective Resistance

Given an undirected graph G, the effective resistance r(s,t) measures the dissimilarity of node pair s,t in G, which finds numerous applications in real-world problems, such as recommender systems, combinatorial optimization, molecular chemistry, and electric power networks. Existing techniques towards pairwise effective resistance estimation either trade approximation guarantees for practical efficiency, or vice versa. In particular, the state-of-the-art solution is based on a multitude of Monte Carlo random walks, rendering it rather inefficient in practice, especially on large graphs. Motivated by this, this paper first presents an improved Monte Carlo approach, AMC, which reduces both the length and amount of random walks required without degrading the theoretical accuracy guarantee, through careful theoretical analysis and an adaptive sampling scheme. Further, we develop a greedy approach, GEER, which combines AMC with sparse matrix-vector multiplications in an optimized and non-trivial way. GEER offers significantly improved practical efficiency over AMC without compromising its asymptotic performance and accuracy guarantees. Extensive experiments on multiple benchmark datasets reveal that GEER is orders of magnitude faster than the state of the art in terms of computational time when achieving the same accuracy.

A new concatenated Multigraph Neural Network for IoT intrusion detection

The last few years have seen a high volume of sophisticated cyber-attacks leading to financial instability and privacy breaches. This reveals the need for a Network Intrusion Detection System (NIDS) that is more robust, effective, and capable of learning complex relations of network flows. Existing machine learning approaches are barely effective for picking new attacks in IoT traffic, primarily due to treating flows independently. Recently, Graph Neural Networks (GNNs) have gained popularity due to their ability to model underlying topology in the form of nodes and edges. We propose a GNN-based NIDS that maximizes the possibility of involving structural characteristics of normal and malicious network traffic. We construct a multi-edged graph structure that captures full communication between any pair of IoT nodes at the edge level. This novel GNN model combines the benefits of spectral and spatial GNNs tailored to process and learn from complex multigraph-structured information. The proposed GNN model is adjusted to work on multi-edges and multi-dimensional edge features. Extensive experimental analysis using evaluation metrics is carried out on four benchmark datasets, demonstrating the competence of our proposed scheme compared to the state-of-the-art GNN models. Our proposed model shows about 2% to 5% improvement in accuracy, precision, F1 and recall offering less training time and model size in the considered datasets. The proposed model has achieved high accuracy ranging from 98.91% to 99.96%, with precision ranging from 98.86 to 99.96, recall ranging from 98.91% to 99.96%, and F1-score ranging from 98.74% to 99.95% in the four benchmark datasets.

Local Phase Transitions in a Model of Multiplex Networks with Heterogeneous Degrees and Inter-Layer Coupling.

Multilayer networks represent multiple types of connections between the same set of nodes. Clearly, a multilayer description of a system adds value only if the multiplex does not merely consist of independent layers. In real-world multiplexes, it is expected that the observed inter-layer overlap may result partly from spurious correlations arising from the heterogeneity of nodes, and partly from true inter-layer dependencies. It is therefore important to consider rigorous ways to disentangle these two effects. In this paper, we introduce an unbiased maximum entropy model of multiplexes with controllable intra-layer node degrees and controllable inter-layer overlap. The model can be mapped to a generalized Ising model, where the combination of node heterogeneity and inter-layer coupling leads to the possibility of local phase transitions. In particular, we find that node heterogeneity favors the splitting of critical points characterizing different pairs of nodes, leading to link-specific phase transitions that may, in turn, increase the overlap. By quantifying how the overlap can be increased by increasing either the intra-layer node heterogeneity (spurious correlation) or the strength of the inter-layer coupling (true correlation), the model allows us to disentangle the two effects. As an application, we show that the empirical overlap observed in the International Trade Multiplex genuinely requires a nonzero inter-layer coupling in its modeling, as it is not merely a spurious result of the correlation between node degrees across different layers.

Opinion Formation on Social Networks—The Effects of Recurrent and Circular Influence

We present a generalised complex contagion model for describing behaviour and opinion spreading on social networks. Recurrent interactions between adjacent nodes and circular influence in loops in the network structure enable the modelling of influence spreading on the network scale. We have presented details of the model in our earlier studies. Here, we focus on the interpretation of the model and discuss its features by using conventional concepts in the literature. In addition, we discuss how the model can be extended to account for specific social phenomena in social networks. We demonstrate the differences between the results of our model and a simple contagion model. Results are provided for a small social network and a larger collaboration network. As an application of the model, we present a method for profiling individuals based on their out-centrality, in-centrality, and betweenness values in the social network structure. These measures have been defined consistently with our spreading model based on an influence spreading matrix. The influence spreading matrix captures the directed spreading probabilities between all node pairs in the network structure. Our results show that recurrent and circular influence has considerable effects on node centrality values and spreading probabilities in the network structure.

ERβ promoted invadopodia formation-mediated non-small cell lung cancer metastasis via the ICAM1/p-Src/p-Cortactin signaling pathway.

In a previous study, our research group observed that estrogen promotes the metastasis of non-small cell lung cancer (NSCLC) through the estrogen receptor β (ERβ). Invadopodia are key structures involved in tumor metastasis. However, it is unclear whether ERβ is involved in the promotion of NSCLC metastasis through invadopodia. In our study, we used scanning electron microscopy to observe the formation of invadopodia following the overexpression of ERβ and treatment with E2. In vitro experiments using multiple NSCLC cell lines demonstrated that ERβ can increase the formation of invadopodia and cell invasion. Mechanistic studies revealed that ERβ can upregulate the expression of ICAM1 by directly binding to estrogen-responsive elements (EREs) located on the ICAM1 promoter, which in turn can enhance the phosphorylation of Src/cortactin. We also confirmed these findings in vivo using an orthotopic lung transplantation mouse model, which validated the results obtained from the in vitro experiments. Finally, we examined the expressions of ERβ and ICAM1 using immunohistochemistry in both NSCLC tissue and paired metastatic lymph nodes. The results confirmed that ERβ promotes the formation of invadopodia in NSCLC cells through the ICAM1/p-Src/p-Cortactin signaling pathway.

Graph Neural Network-Based Efficient Subgraph Embedding Method for Link Prediction in Mobile Edge Computing

Link prediction is critical to completing the missing links in a network or to predicting the generation of new links according to current network structure information, which is vital for analyzing the evolution of a network, such as the logical architecture construction of MEC (mobile edge computing) routing links of a 5G/6G access network. Link prediction can provide throughput guidance for MEC and select appropriate c nodes through the MEC routing links of 5G/6G access networks. Traditional link prediction algorithms are always based on node similarity, which needs predefined similarity functions, is highly hypothetical and can only be applied to specific network structures without generality. To solve this problem, this paper proposes a new efficient link prediction algorithm PLAS (predicting links by analysis subgraph) and its GNN (graph neural network) version PLGAT (predicting links by graph attention networks) based on the target node pair subgraph. In order to automatically learn the graph structure characteristics, the algorithm first extracts the h-hop subgraph of the target node pair, and then predicts whether the target node pair will be linked according to the subgraph. Experiments on eleven real datasets show that our proposed link prediction algorithm is suitable for various network structures and is superior to other link prediction algorithms, especially in some 5G MEC Access networks datasets with higher AUC (area under curve) values.

Sequential path-equilibration algorithm for highly accurate traffic flow assignment in an urban road network

Nowadays, the issue of traffic flow assignment has become an interdisciplinary topic that concerns multiple research areas and branches of science. This work is focussed on the mathematical and computational aspects of the equilibrium traffic assignment problem in the case when route flows are considered to be decision variables. Firstly, we obtain a fixed-point mapping with the explicit contraction operator, which is proven to equilibrate the journey times on feasible routes between a single origin-destination pair of nodes with the quadratic rate. Remarkable that from mathematical perspectives, the developed operator generalizes most path-equilibration operators already exploited by researchers. Secondly, we use the obtained fixed-point procedure to run the sequential path-equilibration algorithm for traffic flow assignment on well-known test urban road networks with arc-additive travel time functions. Our computational results appear to demonstrate higher accuracy of user-equilibrium traffic assignment solutions than the best ones known to us. In other words, developed within this paper sequential path-equilibration algorithm leads to solutions with less goal function values compared to the best solutions for today, according to our knowledge.

Design of soft-error resilient SRAM cell with high read and write stability for robust operations

This paper proposes a highly robust 16 transistor soft-error resilient SRAM cell (SERSC-16T) to provide complete resilience to single event upsets (SEU). The proposed cell is complete resilient to SEU at any sensitive node and also shows recovery from the double-node-upset to its fixed internal node pair. Owing to its separate read path through an internal node, the proposed cell offers the highest read-stability, 6.8 times higher than the state-of-the-art cell RHD-14T. The proposed cell also shows the fastest write operation and its write access time is 1.6 times less compared to the recently proposed cell SCCS-18T. In addition, the proposed cell has 1.7-times higher write stability compared to state-of-the-art cell HP-12T. The SERSC-16T cell also shows moderate leakage power dissipation, which is 1.5 times less compared to the SCCS-18T cell. Moreover, the proposed cell shows the best figure of merit and the most negligible probability of SEU occurrence among all state of the art radiation hardened SRAM cells.

Metapaths: similarity search in heterogeneous knowledge graphs via meta-paths.

Heterogeneous knowledge graphs (KGs) have enabled the modeling of complex systems, from genetic interaction graphs and protein-protein interaction networks to networks representing drugs, diseases, proteins, and side effects. Analytical methods for KGs rely on quantifying similarities between entities, such as nodes, in the graph. However, such methods must consider the diversity of node and edge types contained within the KG via, for example, defined sequences of entity types known as meta-paths. We present metapaths, the first R software package to implement meta-paths and perform meta-path-based similarity search in heterogeneous KGs. The metapaths package offers various built-in similarity metrics for node pair comparison by querying KGs represented as either edge or adjacency lists, as well as auxiliary aggregation methods to measure set-level relationships. Indeed, evaluation of these methods on an open-source biomedical KG recovered meaningful drug and disease-associated relationships, including those in Alzheimer's disease. The metapaths framework facilitates the scalable and flexible modeling of network similarities in KGs with applications across KG learning. The metapaths R package is available via GitHub at https://github.com/ayushnoori/metapaths and is released under MPL 2.0 (Zenodo DOI: 10.5281/zenodo.7047209). Package documentation and usage examples are available at https://www.ayushnoori.com/metapaths.

Joint Active and Passive Beamforming Design for RIS-Aided IBFD IoT Communications: QoS and Power Efficiency Considerations

In a reconfigurable intelligent surface (RIS) aided communication network, a RIS equipped with multiple passive reflecting elements assists in extending the coverage of wireless networks by overcoming the effects of non-line-of-sight propagation. Accordingly, to present the case for utilizing RIS panels in future consumer internet of things (IoT) networks, in this paper, we focus on a RIS-aided IoT network operating in in-band full-duplex (IBFD) mode. Since all the IoT node pairs communicate simultaneously through individual IBFD links at the same time-frequency resources, the nodes suffer from strong self-interference (SI) and inter-node interference. Consequently, in this paper, we investigate a joint active and passive beamforming design at each IoT node and the RIS, respectively, by minimizing the total transmission power of the network, subject to a minimum rate constraint for each IoT node and a constraint that guarantees a unit modulus phase shift at the RIS. As the original joint active and passive beamforming design problem is non-convex and intractable, we decompose the problem into two sub-problems. For a given passive beamformer design, we solve the original problem to obtain the optimal beamforming vectors at each IoT node. Next, for the obtained active beamformer, we propose two algorithms based on i) gradient descent (GD) search and ii) Riemannian conjugate gradient (RCG) to obtain the optimal passive beamformer at the RIS. Through extensive numerical analysis, we verify the effectiveness of the proposed algorithms and also show the effects of using RIS and transmitting in IBFD mode on the average rate and power of the considered consumer IoT network. We investigate the impact of several system parameters such as RIS elements, node pairs, level of hardware impairments at the transmitter and receiver, etc. We also highlight the trade-off between performance improvement and complexity due to elements used at RIS.

Multi-antenna Jammer assisted covert communications in data collected IoT with NOMA

In this paper, we investigate covert communications in data collected IoT with NOMA, where the paired sensor nodes S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> and S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> transmit covert messages to a legitimate receiver (Bob) in the presence of a Warden (Willie). To confuse the detection at Willie, an extra multi-antenna friendly jammer (Jammer) has been employed to transmit artificial noise (AN) with random power. Based on the CSI of Willie is available or not at Jammer, three AN transmission schemes, including null-space artificial noise (NAN), transmit antenna selection (TAS), and zero-forcing beamforming (ZFB), are proposed. Furthermore, the closed-form expressions of expected minimum detection error probability (EMDEP) and joint connection outage probability (JCOP) are derived to measure covertness and reliability, respectively. Finally, the maximum effective covert rate (ECR) is obtained with a given covertness constraint. The numerical results show that ZFB scheme has the best maximum ECR in the case of the number of antennas satisfies N > 2, and the same maximum ECR can be achieved in ZFB and NAN schemes with N =3D 2. Moreover, TAS scheme also can improve the maximum ECR compared with the benchmark scheme (i.e., signal-antenna jammer). In addition, a proper NOMA node pairing can further improve the maximum ECR.

Enhanced security using multiple paths routine scheme in cloud-MANETs

Cloud Mobile Ad-hoc Networks (Cloud-MANETs) is a framework that can access and deliver cloud services to MANET users through their smart devices. MANETs is a pool of self-organized mobile gadgets that can communicate with each other with no support from a central authority or infrastructure. The main advantage of MANETs is its ability to manage mobility while data communication between different users in the system occurs. In MANETs, clustering is an active technique used to manage mobile nodes. The security of MANETs is a key aspect for the fundamental functionality of the network. Addressing the security-related problems ensures that the confidentiality and integrity of the data transmission is secure. MANETs are highly prone to attacks because of their properties.In clustering schemes, the network is broken down to sub-networks called clusters. These clusters can have overlapping nodes or be disjointed. An enhanced node referred to asthe Cluster Head (CH) is chosen from each set to overseetasks related to routing. It decreases the member nodes’ overhead and improvesthe performance of the system. The relationship between the nodes and CH may vary randomly, leading to re-associations and re-clustering in a MANET that is clustered. An efficient and effective routing protocol is required to allow networking and to find the most suitable paths between the nodes. The networking must be spontaneous, infrastructure-less, and provide end-to-end interactions. The aim of routing is the provision of maximum network load distribution and robust networks. This study focused on the creation of a maximal route between a pair of nodes, and to ensure the appropriate and accurate delivery of the packet. The proposed solution ensured that routing can be carried out with the lowest bandwidth consumption. Compared to existing protocols, the proposed solution had a control overhead of 24, packet delivery ratio of 81, the lowest average end-to-end delay of 6, and an improved throughput of 80,000, thereby enhancing the output of the network. Our result shows that multipath routing enables the network to identify alternate paths connecting the destination and source. Routing is required to conserve energy and for optimum bandwidth utilization.

Deep Cross-Network Alignment with Anchor Node Pair Diverse Local Structure

Network alignment (NA) offers a comprehensive way to build associations between different networks by identifying shared nodes. While the majority of current NA methods rely on the topological consistency assumption, which posits that shared nodes across different networks typically have similar local structures or neighbors, we argue that anchor nodes, which play a pivotal role in NA, face a more challenging scenario that is often overlooked. In this paper, we conduct extensive statistical analysis across networks to investigate the connection status of labeled anchor node pairs and categorize them into four situations. Based on our analysis, we propose an end-to-end network alignment framework that uses node representations as a distribution rather than a point vector to better handle the structural diversity of networks. To mitigate the influence of specific nodes, we introduce a mask mechanism during the representation learning process. In addition, we utilize meta-learning to generalize the learned information on labeled anchor node pairs to other node pairs. Finally, we perform comprehensive experiments on both real-world and synthetic datasets to confirm the efficacy of our proposed method. The experimental results demonstrate that the proposed model outperforms the state-of-the-art methods significantly.