Partition Of Nodes Research Articles

Network community detection and clustering with random walks

We present an approach to partitioning network nodes into nonoverlapping communities, a key step in revealing network modularity and functional organization. Our methodology, applicable to networks with weighted or unweighted symmetric edges, uses random walks to explore neighboring nodes in the same community. The walk-likelihood algorithm (WLA) produces an optimal partition of network nodes into a given number of communities. The walk-likelihood community finder employs WLA to predict both the optimal number of communities and the corresponding network partition. We have extensively benchmarked both algorithms, finding that they outperform or match other methods in terms of the modularity of predicted partitions and the number of links between communities. Making use of the computational efficiency of our approach, we investigated a large-scale map of roads and intersections in the state of Colorado. Our clustering yielded geographically sensible boundaries between neighboring communities.

Observability, dominance, and induction in learning models

Learning models do not in general imply that weakly dominated strategies are irrelevant or justify the related concept of “forward induction,” because rational agents may use dominated strategies as experiments to learn how opponents play, and may not have enough data to rule out a strategy that opponents never use. Learning models also do not support the idea that the selected equilibria should only depend on a game's reduced normal form. However, playing the extensive form of a game is equivalent to playing the normal form augmented with the appropriate terminal node partitions so that two games are information equivalent, i.e., the players receive the same feedback about others' strategies.

A Blockchain Storage Architecture Based on Information-Centric Networking

Blockchain technology is a unique distributed ledger technology that has been widely used in various areas. With the increase in data on the blockchain and the append-only nature of the blockchain, the traditional blockchain’s full replica storage technique leads to blockchain storage scalability problem. Existing methods prioritize minimizing the storage strain on blockchain nodes while ignoring the availability of data, resulting in a lengthy average response time for users to access the blockchain. To address the shortcomings, this paper proposes an Information-Centric Networking-based blockchain storage architecture. The architecture uses the enhanced resolution system for community division to build blockchain node partitions and store blockchain ledgers in the underlying network. It introduces virtual chain for rapid blockchain indexing and adopts a collaborative block replica deletion algorithm across neighboring partitions, including replica number decision based on blockchain access decay characteristics and replica deletion based on resource relationship. Finally, we compare and analyze the proposed blockchain storage architecture with BC-store and KASARASA, and the results demonstrate that this architecture has significantly lower average access time than others. The replica data volume of this method is reduced by 57.2% compared to the full replica policy, but the access time is only 5.2% slower when compared to the full replica policy, which substantially increases the replica storage utilization.

A New Heuristic Algorithm for Multi Vehicle Routing Problem with AND/OR-Type Precedence Constraints and Hard Time Windows

In this paper the classic known Multi Vehicle Routing Problem (VRP) is studied where classically several vehicles are set in a central depot, depending on the allocation strategy, each vehicle starts traveling to visit a set of nodes one after another to provide a service of gathering or delivering commodities with the aim of minimizing total traveling distances and costs. In the current paper, this classic problem is extended by new approach of AND/OR precedence constraints (PC) which have not been considered so far in the related literature. Traditionally, PC have been considered in VRPs as the 'AND' type, where the immediate successor of a node cannot be visited until its predecessor nodes have reached their end of services. However by additional OR-type precedence constraints, there are some interconnected nodes through the concept of OR, therein no mandatory need to visit all predecessors of a successor node is acquired before it can be met, and only finishing a part of them can let to that particular node to get visited. This fact is widely observed in pickup and routing and distribution real cases where requisites for some specific products can be fulfilled via various potential suppliers. Implementation of this type of PC graph in VRP is considered as the first introduction and application in the category of this problem. So, initially, the problem is mathematically formulated, then, due to problem’s NP-hard complexity and allocation-routing characteristics, a decomposition-based technique is utilized to solve the problem. The procedure is based on recently enhanced Benders’ decomposition approach named as Branch and Search Algorithm, partitioning the original main problem into allocation and routing parts. Unlike the previous version of Benders algorithm, logic based, this newly promoted method acts in a way that at the allocation level, it generates partition of nodes with feasible solutions in lower routing level. The routing part itself has been enhanced by heuristics to cover AND/OR PC graphs. Furthermore, the efficiency of the proposed solution procedure is tested and verified by running on several generated problems in different sizes and in the larger scale it is implemented on the real case of a distribution company in Iran.

Symmetry-driven network reconstruction through pseudobalanced coloring optimization

Symmetries found through automorphisms or graph fibrations provide important insights in network analysis. Symmetries identify clusters of robust synchronization in the network which improves the understanding of the functionality of complex biological systems. Network symmetries can be determined by finding a balanced coloring of the graph, which is a node partition in which each cluster of nodes receives the same information (color) from the rest of the graph. In recent work we saw that biological networks such as gene regulatory networks, metabolic networks and neural networks in organisms ranging from bacteria to yeast and humans are rich in fibration symmetries related to the graph balanced coloring. Networks based on real systems, however, are built on experimental data which are inherently incomplete, due to missing links, collection errors, and natural variations within specimens of the same biological species. Therefore, it is fair to assume that some of the existing symmetries were not detected in our analysis. For that reason, a method to find pseudosymmetries and repair networks based on those symmetries is important when analyzing real world networks. In this paper we introduce the pseudobalanced coloring (PBCIP) problem, and provide an integer programming formulation which (a) calculates a PBCIP of the graph taking into account the missing data, and (b) optimally repairs the graph with the minimal number of added/removed edges to maximize the symmetry of the graph. We apply our formulation to the C. elegans connectome to find pseudocoloring and the optimal graph repair. Our solution compares well with a manually curated ground-truth C. elegans graph as well as solutions generated by other methods of missing link prediction. Furthermore, we provide an extension of the algorithm using Bender’s decomposition that allows our formulation to be applied to larger networks.

Pushing Collaborative Data Deduplication to the Network Edge: An Optimization Framework and System Design

Edge computing has become a new computing paradigm with explosive growth in recent years. We consider the problem of pushing data deduplication to the network edge and propose a new framework for distributed edge-facilitated deduplication (EF-dedup). Deduplication at the network edge allows us to exploit the high degree of geographic- and temporal-correlation in edge data to achieve space efficiency. By leveraging distributed computing power available on the edge in a collaborative fashion, the edge nodes can effectively suppress duplicated edge data, consuming considerably less space and WAN bandwidth. To this end, we partition the edge nodes into disjoint collaborative clusters, maintain a deduplication index structure across them using a distributed key-value store and perform deduplication within those clusters. However, this partitioning problem is very challenging and requires the optimization of a novel tradeoff: edge nodes with highly correlated data may not always be within the same edge cloud, with non-trivial network cost among them. We formulate a joint storage and network optimization problem with different design objectives, such as arbitrary partitioning and balanced partitioning of edge nodes. The problem is shown to be NP-Hard in general. Then, an optimization framework with efficient algorithms is developed and is proven to achieve a closed-form competitive ratio. Our experiments, performed on edge nodes in a corporate lab <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> and a central cloud at AWS, demonstrate that EF-dedup achieves 67.4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 133.7% better deduplication throughput than sole cloud-based techniques and achieves 20.0-62.6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> lesser aggregate cost in terms of the network-storage trade-off as compared to approaches that solely favor one over the other.

CARMI

Learned indexes, which use machine learning models to replace traditional index structures, have shown promising results in recent studies. However, existing learned indexes exhibit a performance gap between synthetic and real-world datasets, making them far from practical indexes. In this paper, we identify that ignoring the importance of data partitioning during model training is the main reason for this problem. Thus, we explicitly apply data partitioning to index construction and propose a new efficient and updatable cache-aware RMI framework, called CARMI. Specifically, we introduce entropy as a metric to quantify and characterize the effectiveness of data partitioning of tree nodes in learned indexes and propose a novel cost model, laying a new theoretical foundation for future research. Then, based on our novel cost model, CARMI can automatically determine tree structures and model types under various datasets and workloads by a hybrid construction algorithm without any manual tuning. Furthermore, since memory accesses limit the performance of RMIs, a new cache-aware design is also applied in CARMI, which makes full use of the characteristics of the CPU cache to effectively reduce the number of memory accesses. Our experimental study shows that CARMI performs better than baselines, achieving an average of 2.2X/1.9X speedup compared to B+ Tree/ALEX, while using only about 0.77X memory space of B+ Tree. On the SOSD platform, CARMI outperforms all baselines, with an average speedup of 1.2X over the nearest competitor RMI, which has been carefully tuned for each dataset in advance.

A Light Signaling Approach to Node Grouping for Massive MIMO IoT Networks

Massive MIMO is one of the leading technologies for connecting very large numbers of energy-constrained nodes, as it offers both extensive spatial multiplexing and large array gain. A challenge resides in partitioning the many nodes into groups that can communicate simultaneously such that the mutual interference is minimized. Here we propose node partitioning strategies that do not require full channel state information, but rather are based on nodes’ respective directional channel properties. In our considered scenarios, these typically have a time constant that is far larger than the coherence time of the channel. We developed both an optimal and an approximation algorithm to partition users based on directional channel properties, and evaluated them numerically. Our results show that both algorithms, despite using only these directional channel properties, achieve similar performance in terms of the minimum signal-to-interference-plus-noise ratio for any user, compared with a reference method using full channel knowledge. In particular, we demonstrate that grouping nodes with related directional properties is to be avoided. We hence realize a simple partitioning method, requiring minimal information to be collected from the nodes, and in which this information typically remains stable over the long term, thus promoting the system’s autonomy and energy efficiency.

Detecting mesoscale structures by surprise

The importance of identifying mesoscale structures in complex networks can be hardly overestimated. So far, much attention has been devoted to detect modular and bimodular structures on binary networks. This effort has led to the definition of a framework based upon the score function called ‘surprise’, i.e. a p-value that can be assigned to any given partition of nodes. Hereby, we make a step further and extend the entire framework to the weighted case: six variants of surprise, induced by just as many variants of the hypergeometric distribution, are, thus, considered. As a result, a general, statistically grounded approach for detecting mesoscale network structures via a unified, suprise-based framework is presented. To illustrate its performances, both synthetic benchmarks and real-world configurations are considered. Moreover, we attach to the paper a Python code implementing all variants of surprise discussed in the present manuscript.

Dynamic Naming Scheme and Lookup Method Based on Trie for Vehicular Named Data Network

Content naming and lookup are decisive functions of the future architecture named data network (NDN). The core concept of NDN is the content distribution between consumers and content providers. The NDN supports advance vehicular networks that is famous with vehicular-named data network (VNDN) with different naming schemes such as hybrid, flat, attribute-based, and hierarchical names. These schemes are used in a static way for vehicular network, in summary, the hybrid, flat, and attribute-based makes a complex structure, and on the other hand, hierarchical names long in length and name lookup performance are a bottleneck in NDN, which can directly affect the network performance. Therefore, we introduce a dynamic naming scheme and lookup method (DNSL) for VNDN to mitigate these issues. We argue that the dynamic naming scheme is a better approach to VNDN, while the static name is a cost-effective, hefty, integrated fashion, and improper for the vehicular network. This study focuses on (1) a dynamic naming scheme using dynamic-tag and (2) a lookup method based on node partition of trie; the trie approach is very famed in data structure and extensively used for the lookup content, insertion, and deletion processes. Our experimental evaluation shows that the DNSL scheme is highly efficient, scalable, and provably correct for VNDN.

Power Balance Partition Control Based on Topology Characteristics of Multi-Source Energy Storage Nodes

Aiming at the power balance control of multi-source energy storage grid in the case of a high proportion of new energy grid connection. In this article, a power grid dynamic partition method based on the Markov energy field principle and a priori knowledge model is proposed. Combined with the coordinated dispatching of power grid source-load, a two-layer power balance partition control model based on the topological characteristics of multi-source energy storage nodes is established. First, in the upper-layer model, the energy homogenization method of multi-source energy storage nodes is studied, and the Markov energy field model of power grid node partition based on energy interaction constraints between nodes is established to partition the power grid initially. Combined with the prior model of node dynamic partition, the initial partition is dynamically optimized to realize the dynamic partition of the multi-source energy storage grid. Then, in the lower-layer model, the source-load coordinated dispatching model in the power grid partition area is established to realize the dynamic partition control of the power grid. Finally, based on the real operation data of a northeast power grid and IEEE39 node system, a dynamic partition power control simulation model of a multi-source energy storage power grid is established. The simulation results and analysis show that the dynamic partition power control strategy proposed in this article can effectively improve the regulation ability and economy of the power grid.

Improved PBFT Algorithm Based on Vague Sets

The traditional PBFT consensus algorithm has several limitations in the consortium blockchain environment, such as unclear selection of primary node, excessive communication times, etc. To solve these limitations, an improved consensus algorithm VS-PBFT based on vague sets was proposed. VS-PBFT has three phases: node partition, primary node selection, and global consensus. Firstly, the nodes of the whole network are partitioned using the consistent hashing-like consensus algorithm, and then the local primary node is selected by the primary node selection algorithm in each partition. The local primary nodes run the four-phase PBFT consensus algorithm to complete the global consensus. The analysis of the VS-PBFT consistency algorithm shows that the algorithm can improve the fault-tolerant rate and reduce communication complexity, and the algorithm is dynamic; that is, node can join and quit adaptively.

Representative community divisions of networks

Methods for detecting community structure in networks typically aim to identify a single best partition of network nodes into communities, often by optimizing some objective function, but in real-world applications there may be many competitive partitions with objective scores close to the global optimum and one can obtain a more informative picture of the community structure by examining a representative set of such high-scoring partitions than by looking at just the single optimum. However, such a set can be difficult to interpret since its size can easily run to hundreds or thousands of partitions. In this paper we present a method for analyzing large partition sets by dividing them into groups of similar partitions and then identifying an archetypal partition as a representative of each group. The resulting set of archetypal partitions provides a succinct, interpretable summary of the form and variety of community structure in any network. We demonstrate the method on a range of example networks.

Achieving Graph Clustering Privacy Preservation Based on Structure Entropy in Social IoT

Decoding the real structure from the Social Internet-of-Things (SIoT) network with a large-scale noise structure plays a fundamental role in data mining. Protecting private information from leakage in the mining process and obtaining accurate mining results is a significant challenge. To tackle this issue, we present a graph clustering privacy-preserving method based on structure entropy, which combines data mining with the structural information theory. Specially, user private information in SIoT is encrypted by Brakerski–Gentry–Vaikuntanathan (BGV) homomorphism to generate a graph structure in the ciphertext state, the ciphertext graph structure is then divided into different modules by applying a 2-D structural information solution algorithm and a entropy reduction principle node module partition algorithm, and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -dimensional structural information solution algorithm is utilized to further cluster the internal nodes of the partition module. Moreover, normalized structural information and network node partition similarity are introduced to analyze the correctness and similarity degree of clustering results. Finally, security analysis and theoretical analysis indicate that this scheme not only guarantees the correctness of the clustering results but also improves the security of private information in SIoT. Experimental evaluation and analysis shows that the clustering results of this scheme have higher efficiency and reliability.

An ensemble model to optimize modularity in dynamic bipartite networks

Distinct non-random quantitative interactions at diverse timestamps formulate real-world dynamic complex networks. The most frequently used class of methods for discovering communities in dynamic networks is modularity optimization that evaluates the quality of the partition of network nodes into distinct communities. The bipartite networks have bipartite modularity and bipartite modularity optimization respectively. Newman's modularity is a consistently used algorithm to evaluate modules of unipartite networks yet it is ineffective for assessing the division of bipartite networks with two types of vertices. Many community detection methods suggest bipartite modularity to accommodate this issue. They usually employ information about the existence or lack of interactions between nodes. In quantitative networks, weighted modularity is a potential approach for measuring the quality of community partitions (Lu et al. IEEE, 179–184, 2013). This study offers an ensemble model for detecting one-mode communities and optimizing modularity in dynamic bipartite weighted networks. By using collaborative weighted projection, bipartite networks get projected into two weighted one-mode networks. The results of experiments both on real-world dynamic network data and synthetic data demonstrate that the modularity of the method is significantly greater than that of current techniques and the communities discovered contain vertices of comparable kinds exhibiting the suggested algorithm's performance is ample.

Skeleton-Based ST-GCN for Human Action Recognition With Extended Skeleton Graph and Partitioning Strategy

Skeleton-based Graph Convolutional Networks (GCN) for human action and interaction recognition have received considerable attention of researchers due to its compact and view-invariant nature of skeleton data. However, the static skeleton graph topology in conventional GCNs does not reflect the implicit relationships of non-adjacent joints, which contain vital latent information for a skeleton pose in an action sequence. Moreover, traditional tri-categorical node partitioning strategy discards much of the motion dependencies along temporal dimension for non-physically connected edges. We propose an extended skeleton graph topology along with extended partitioning strategy to extract much of the non-adjacent joint relational information in the model for robust discriminative features. Extended skeleton graph represents joints as vertices and weighted edges represent intrinsic and extrinsic relationships between physically connected and non-physically connected joints respectively. Furthermore, extended partitioning strategy divides the input graph for GCN as five-categorical fixed-length tensor to encompass maximal motion dependencies. Finally, the extended skeleton graph and partitioning strategy are realized by adopting Spatio-Temporal Graph Convolutional Network (ST-GCN). The experiments carried out over three large scale datasets NTU-RGB+D, NTU-RGB+D 120 and Kinetics-Skeleton show improved performance over conventional state-of-the-art ST-GCNs.

Optimization of Clustering in Wireless Sensor Networks: Techniques and Protocols

Recently, Wireless Sensor Network (WSN) technology has emerged extensively. This began with the deployment of small-scale WSNs and progressed to that of larger-scale and Internet of Things-based WSNs, focusing more on energy conservation. Network clustering is one of the ways to improve the energy efficiency of WSNs. Network clustering is a process of partitioning nodes into several clusters before selecting some nodes, which are called the Cluster Heads (CHs). The role of the regular nodes in a clustered WSN is to sense the environment and transmit the sensed data to the selected head node; this CH gathers the data for onward forwarding to the Base Station. Advantages of clustering nodes in WSNs include high callability, reduced routing delay, and increased energy efficiency. This article presents a state-of-the-art review of the available optimization techniques, beginning with the fundamentals of clustering and followed by clustering process optimization, to classifying the existing clustering protocols in WSNs. The current clustering approaches are categorized into meta-heuristic, fuzzy logic, and hybrid based on the network organization and adopted clustering management techniques. To determine clustering protocols’ competency, we compared the features and parameters of the clustering and examined the objectives, benefits, and key features of various clustering optimization methods.

Cluster synchronization of networks via a canonical transformation for simultaneous block diagonalization of matrices.

We study cluster synchronization of networks and propose a canonical transformation for simultaneous block diagonalization of matrices that we use to analyze the stability of the cluster synchronous solution. Our approach has several advantages as it allows us to: (1) decouple the stability problem into subproblems of minimal dimensionality while preserving physically meaningful information, (2) study stability of both orbital and equitable partitions of the network nodes, and (3) obtain a parameterization of the problem in a small number of parameters. For the last point, we show how the canonical transformation decouples the problem into blocks that preserve key physical properties of the original system. We also apply our proposed algorithm to analyze several real networks of interest, and we find that it runs faster than alternative algorithms from the literature.

World War III analysis using signed social networks

In the recent period of time with a lot of social platforms emerging, the relationships among various units can be framed with respect to either positive, negative or no relation. These units can be individuals, countries or others that form the basic structural component of a signed network. These signed networks picture a dynamic characteristic of the graph so formed allowing only few combinations of signs that brings the structural balance theorem in picture. Structural balance theory affirms that signed social networks tend to be organized so as to avoid conflictual situations, corresponding to cycles of unstable relations. The aim of structural balance in networks is to find proper partitions of nodes that guarantee equilibrium in the system allowing only few combination triangles with signed edges to be permitted in graph. Most of the works in this field of networking have either explained the importance of signed graph or have applied the balance theorem and tried to solve problems. Following the recent time trends with each nation emerging to be superior and competing to be the best, the probable doubt of happening of WW-III(World War-III) comes into every individuals mind. Nevertheless, our paper aims at answering some of the interesting questions on World War-III. In this project we have worked with the creation of a signed graph picturing the World War-III participating countries as nodes and have predicted the best possible coalition of countries that will be formed during war. Also, we have visually depicted the number of communities that will be formed in this war and the participating countries in each communities.

On community structure validation in real networks

Community structure is a commonly observed feature of real networks. The term refers to the presence in a network of groups of nodes (communities) that feature high internal connectivity, but are poorly connected between each other. Whereas the issue of community detection has been addressed in several works, the problem of validating a partition of nodes as a good community structure for a real network has received considerably less attention and remains an open issue. We propose a set of indices for community structure validation of network partitions that are based on an hypothesis testing procedure that assesses the distribution of links between and within communities. Using both simulations and real data, we illustrate how the proposed indices can be employed to compare the adequacy of different partitions of nodes as community structures in a given network, to assess whether two networks share the same or similar community structures, and to evaluate the performance of different network clustering algorithms.