Cube Network Research Articles

Assessing reliability in Complete Josephus Cube networks via strongly Menger edge-connectivity

Assessing reliability in Complete Josephus Cube networks via strongly Menger edge-connectivity

Connectivity and diagnosability of the complete Josephus cube networks under h-extra fault-tolerant model

The h-extra connectivity and the h-extra diagnosability are key parameters for evaluating the reliability and fault-tolerance of the interconnection networks of the multiprocessor systems, and play an important role in designing and maintaining interconnection networks. Recently, various self-diagnostic models have emerged to assess the fault-tolerance in interconnection networks. These interconnection networks are typically expressed by a connected graph G(V,E). For a non-complete graph G and h≥0, the h-extra cut signifies a vertex subset R of G, whose removal results in G−R disconnected, with each remaining component containing at least h+1 vertices. And the h-extra connectivity of G is defined as the minimum cardinality of all h-extra cuts of G. The h-extra diagnosability for a graph G denotes the maximum number of detectable faulty vertices when focusing on these h-extra faulty sets only. The complete Josephus cube CJCn, a variant of Qn, exhibits superior properties compared to hypercube Qn, and also boasts higher connectivity. In this study, with the help of the exact value of the h-extra connectivity of CJCn, the explicit expression of h-extra diagnosability of CJCn under both the PMC model for n≥5 and 1≤h≤⌊n−32⌋ and the MM* model for n≥5 and 2≤h≤⌊n−32⌋ are identified to share the same value (h+1)n−(h−12)+1.

High fault-tolerant performance of the divide-and-swap cube network

Two crucial metrics used to evaluate the fault tolerance of interconnection networks are connectivity and diagnosability. By improving the connectivity and diagnosability of the interconnection network, its fault tolerance can be enhanced. In this paper, we focus on determining the g-extra connectivity (0≤g≤10) of the divide-and-swap cube DSCn, as well as its diagnosability based on the pessimistic diagnosis strategy and g-extra precise diagnosis strategy, under the PMC and MM* models. The research analysis suggests that compared with some other connectivity and diagnosability of DSCn, such as classical connectivity, structure connectivity, super connectivity, and classical diagnosability, the extra connectivity/diagnosability and pessimistic diagnosability of DSCn enable it to have a higher fault tolerance. Moreover, we propose two O(Nlog2⁡N) effective diagnosis algorithms of DSCn: the g-extra diagnosis algorithm (EX-DiagnosisDSCn) and the pessimistic diagnosis algorithm (PE-DiagnosisDSCn), where the EX-DiagnosisDSCn algorithm can accurately diagnose the state of all processors in DSCn.

Embedding spanning disjoint cycles in augmented cube networks with prescribed vertices in each cycle

One of the important issues in evaluating an interconnection network is to study the Hamiltonian cycle embedding problems. For a positive integer k, a graph G is said to be spanning k-cyclable if for k prescribed vertices , there exist k disjoint cycles such that the union of spans G, and each contains exactly one vertex of . According to the definition, the problem of finding hamiltonian cycle focuses on k = 1. The notion of spanning cyclability can be applied to the problem of identifying faulty processors and other related issues in interconnection networks. The n-dimensional augmented cube is an important node-symmetric variant of the n-dimensional hypercube . In this paper, we prove that with is spanning k-cyclable for .

A High-Performantal and Server-Centric Based Data Center Network

With the increasing demand of data center interconnection in the network cloud era, data center networks (DCNs) play key roles in computing and communication, becoming the center of a great deal of resources and business. Therefore, how to design a DCN with good performance has been a significant issue in networks. The hypercube is a popular interconnection network topology with low diameter, symmetry and recursive structure, and scalability. As a variant of the hypercube, the crossed cube not only retains the excellent properties of the hypercube, but also performs better in terms of Hamiltonian-connectivity, embeddability, diameter, etc. In this paper, we first propose a novel and server-centric DCN, called CSDC, which is based on the crossed cube network. The performance of CSDC can be characterized by the properties of its logical structure, so we then give its logical structure <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{n}$</tex-math></inline-formula> , and determine the connectivity and edge-connectivity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{n}$</tex-math></inline-formula> . Furthermore, we explore the fault-tolerant paths and disjoint paths between any two distinct nodes in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{n}$</tex-math></inline-formula> , and obtain the diameter of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{n}$</tex-math></inline-formula> . Moreover, we propose a method to construct two completely independent spanning trees (CISTs) in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{n}$</tex-math></inline-formula> . Extensive evaluations demonstrate that CSDC is a magnetic DCN for building large-scale data centers.

Robustness of subsystem reliability of $k$-ary $n$-cube networks under probabilistic fault model

With the emergence of the Big Data era, as multiprocessor systems consisting of multiple processors play a vital role in big data analytics, we are prompted to explore the qualitative and quantitative metric to characterize the reliability of the systems. As the size of the multiprocessor systems grows, the probability of the occurrence of failing processors increases. One metric of the macroscopic reliability of a system is the measure of the collective effect when its subsystems are out of function. The subsystem reliability of a system is the quantitative metric that a fault-free subsystem of specific size is operational as before with the occurrence of individual faults. Although some networks have the same order and similar topologies, there are differences in their subsystem reliabilities. In this work, we focus on the comparison of two distinct topologies of <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-ary <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-cube networks with the same order and calculate the robustness of reliability bounds of <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-ary <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-cube networks. We analytically show that the subsystem reliability is negatively correlated with the dimension <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>, even if two subsystems of <inline-formula><tex-math notation="LaTeX">$Q_{n}^{k}$</tex-math></inline-formula> are of the same order. That is, the smaller <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is, the larger subsystem reliability of <inline-formula><tex-math notation="LaTeX">$Q_{n}^{k}$</tex-math></inline-formula> will be. This work provides a theoretical methodology to choose the more dependable topology of <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-ary <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-cube networks with the same order. Finally, we apply some numerical simulations to validate the results we established.

The generalized 4-connectivity of folded Petersen cube networks

&lt;abstract&gt;&lt;p&gt;The generalized $ \ell $-connectivity $ \kappa_{\ell}(G) $ of a graph $ G $ is a generalization of classical connectivity $ \kappa(G) $ with $ \kappa_{2}(G) = \kappa(G) $. It serves to measure the capability of connection for any $ \ell $ vertices. The folded Petersen cube network $ FPQ_{n, k} $ can be used to model the topological structure of a communication-efficient multiprocessor. This paper shows that the generalized 4-connectivity of the folded Petersen cube network $ FPQ_{n, k} $ is $ n+3k-1 $. As a corollary, the generalized 3-connectivity of $ FPQ_{n, k} $ also is obtained and the results on the generalized 4-connectivity of hypercube $ Q_n $ and folded Petersen graph $ FP_k $ can be verified. These conclusions provide a foundation for studying the generalized 4-connectivity of Cartesian product graphs.&lt;/p&gt;&lt;/abstract&gt;

Sentence Semantic Matching Based on 3D CNN for Human–Robot Language Interaction

The development of cognitive robotics brings an attractive scenario where humans and robots cooperate to accomplish specific tasks. To facilitate this scenario, cognitive robots are expected to have the ability to interact with humans with natural language, which depends on natural language understanding ( NLU ) technologies. As one core task in NLU, sentence semantic matching ( SSM ) has widely existed in various interaction scenarios. Recently, deep learning–based methods for SSM have become predominant due to their outstanding performance. However, each sentence consists of a sequence of words, and it is usually viewed as one-dimensional ( 1D ) text, leading to the existing available neural models being restricted into 1D sequential networks. A few researches attempt to explore the potential of 2D or 3D neural models in text representation. However, it is hard for their works to capture the complex features in texts, and thus the achieved performance improvement is quite limited. To tackle this challenge, we devise a novel 3D CNN-based SSM ( 3DSSM ) method for human–robot language interaction. Specifically, first, a specific architecture called feature cube network is designed to transform a 1D sentence into a multi-dimensional representation named as semantic feature cube. Then, a 3D CNN module is employed to learn a semantic representation for the semantic feature cube by capturing both the local features embedded in word representations and the sequential information among successive words in a sentence. Given a pair of sentences, their representations are concatenated together to feed into another 3D CNN to capture the interactive features between them to generate the final matching representation. Finally, the semantic matching degree is judged with the sigmoid function by taking the learned matching representation as the input. Extensive experiments on two real-world datasets demonstrate that 3DSSM is able to achieve comparable or even better performance over the state-of-the-art competing methods.

Optimal network dimensions for energy conservation in clustered 3D WSN

In this paper, the optimal network dimensions of clustered-routing three-dimensional (3D) wireless sensor networks is provided. The derivation for such dimensions is based upon the minimum energy consumption cost function in the network. Two 3D network geometries are considered, namely, cuboid and cylinder networks. Analysis and simulations have shown that the minimum energy consumption of the two 3D geometries occurs in special dimensions setup. First, for the cuboid network the optimal network dimensions occur at equal length width and height. We refer to this network as cube network. Second, for the cylinder network the optimal case occurs when the radius of the network is around 68.4% of its height. The results are verified using simulations. Low energy adaptive clustering hierarchy protocol has been used as the underlining routing protocol in 3D environment. Total network remaining energy, stable region and network throughput are utilized for performance evaluation of the results. It is shown that networks with optimal dimensions achieve maximum network lifetime and throughput with minimum energy consumption. Moreover, in the optimal network dimensions settings the cylinder network utilizes energy more efficiently and outperforms the cube network in terms of network lifetime and throughput.

Fractional Matching Preclusion for Folded Petersen Cube Networks

Let F be an edge set and F′ a subset of edges and/or vertices of a graph G. Then F is a fractional matching preclusion(FMP) set (F′ is a fractional strong matching preclusion (FSMP) set) if G − F (G − F′) does not contain fractional perfect matching. The FMP(FSMP) number of G is the minimum size of FMP(FSMP) sets of G. The concept of matching preclusion was introduced by Brigham et al., as a measure of robustness in the event of edge failure in interconnection networks. An interconnection network of a larger MP number may be considered as more robust in the event of link failures. The problem of fractional matching preclusion is a generalization of matching preclusion. In this paper, we obtain the FMP and FSMP number for the folded Petersen cube networks. All the optimal fractional strong matching preclusion sets of these graphs are categorized.

Decoupled synchronized states in networks of linearly coupled limit cycle oscillators

Networks of limit cycle oscillators can show intricate patterns of synchronization such as splay states and cluster synchronization. Here we analyze dynamical states that display a continuum of seemingly independent splay clusters. Each splay cluster is a block splay state consisting of sub-clusters of fully synchronized nodes with uniform amplitudes. Phases of nodes within a splay cluster are equally spaced, but nodes in different splay clusters have an arbitrary phase difference that can be fixed or evolve linearly in time. Such coexisting splay clusters form a decoupled state in that the dynamical equations become effectively decoupled between oscillators that can be physically coupled. We provide the conditions that allow the existence of particular decoupled states by using the eigendecomposition of the coupling matrix. Additionally, we provide an algorithm to search for admissible decoupled states using the external equitable partition and orbital partition considerations combined with symmetry groupoid formalism. Unlike previous studies, our approach is applicable when existence does not follow from symmetries alone and also illustrates the differences between adjacency and Laplacian coupling. We show that the decoupled state can be linearly stable for a substantial range of parameters using a simple eight-node cube network and its modifications as an example. We also demonstrate how the linear stability analysis of decoupled states can be simplified by taking into account the symmetries of the Jacobian matrix. Some network structures can support multiple decoupled patterns. To illustrate that, we show the variety of qualitatively different decoupled states that can arise on two-dimensional square and hexagonal lattices.

A network of cubes opens the door for new COF chemistry

Covalent organic frameworks (COFs) offer many of the benefits of metal-organic frameworks (MOFs) yet haven’t kept pace with the growing number of complex architectures achieved by their metal-conta...

Compact and Power-efficient Sobel Edge Detection with Fully Connected Cube-network-based Stochastic Computing

Stochastic computing, an approximate computing method using bitstreams, has attracted attention as an alternative to deterministic computing. Stochastic computing circuits are known to perform complex calculations with high density through probability calculations. Herein, we describe the design of an accurate and compact arithmetic circuit based on stochastic computing. First, we propose a simple technique to change the output of a random number generator that is an integral part of stochastic computing for stochastic multipliers and adders. Compared with conventional designs, the results indicate that the proposed design reduces power and area and enhances the performance. This method uses a fully connected cube network and does not lose accuracy without overhead. Subsequently, when applying this design to image processing in the real world, a 63% area reduction and 95% power savings are achieved when compared to an accurate operator. Therefore, it is clear that the proposed design is optimized for energy-efficient hardware designs with high imprecision tolerance.

A network of cubes opens the door for new COF chemistry

A network of cubes opens the door for new COF chemistry

ANALISIS KEMAMPUAN SPASIAL SISWA BERKEMAMPUAN MATEMATIKA TINGGI DALAM MENYELESAIKAN MASALAH GEOMETRI BANGUN RUANG SISI DATAR

Abstract: This research aims to describe the spatial ability of grade VIII students SMP Kristen GPID Palu in Solving Flat Geometry Problems in Flat-Side Space Based on High. The type of this research is a case study research with a qualitative approach. The subject that use in this research are the students who have high mathematical abilities (ST). The research subjects were given geometry tests to construct a flat side space problem I and then interviewed. To test the credibility of the data, time triangulation was carried out by giving geometry tests to construct the flat side space of problem II and conducting interviews. Based on the results of the analysis it was found that in spatial perception ability, ST were able to determine unit cubes located in the horizontal position and vertical position in the cube stack after being manipulated. Besides that for mental rotation ability, ST is able to rotate the position of the cube and imagine the rotation of the cube correctly. ST determines the change of the cube after being rotated 900 counterclockwise by imagining rotating the cube right to the left. As well as in spatial visualization ability, ST is able to determine the change of cubes into different forms and recognize changes in position of the elements of the cube. ST is able to determine the location of the triangle, circle, and quadrilateral image in the cube network that shows the inside of the cube after being rotated twice.&#x0D;

Connectivity and super connectivity of the divide-and-swap cube

The divide-and-swap cube network is a new hypercube variant network proposed recently. Compared to hypercube, it keeps the same number of vertices and the same asymptotic performances for fundamental algorithms while reducing the network cost. Connectivity and super connectivity are important indices to measure the reliability of networks. In this work, we get the connectivity and super connectivity of divide-and-swap cube network.

Unpaired Many-to-Many Disjoint Path Covers on Bipartite k-Ary n-Cube Networks with Faulty Elements

The [Formula: see text]-ary [Formula: see text]-cube network is known as one of the most attractive interconnection networks for parallel and distributed systems. A many-to-many [Formula: see text]-disjoint path cover ([Formula: see text]-DPC for short) of a graph is a set of [Formula: see text] vertex-disjoint paths joining two disjoint vertex sets [Formula: see text] and [Formula: see text] of equal size [Formula: see text] that altogether cover every vertex of the graph. The many-to-many [Formula: see text]-DPC is classified as paired if each source in [Formula: see text] is further required to be paired with a specific sink in [Formula: see text], or unpaired otherwise. In this paper, we consider the unpaired many-to-many [Formula: see text]-DPC problem of faulty bipartite [Formula: see text]-ary [Formula: see text]-cube networks [Formula: see text], where the sets [Formula: see text] and [Formula: see text] are chosen in different parts of the bipartition. We show that, every bipartite [Formula: see text], under the condition that [Formula: see text] or less faulty edges are removed, has an unpaired many-to-many [Formula: see text]-DPC for any [Formula: see text] and [Formula: see text] subject to [Formula: see text]. The bound [Formula: see text] is tight here.

A Novel Low Cost Interconnection Architecture Based on the Generalized Hypercube

The generalized hypercube (GH) is one key interconnection network with excellent topological properties. It contains many other interconnection topologies, such as the hypercube network, the complete graph, the mesh network, and the $k$ k -ary $n$ n -cube network. It can also be used to construct some data center networks, such as HyperX, BCube, FBFLY, and SWCube. However, the construction cost of GH is high since it contains too many links. In this paper, we propose a novel low cost interconnection architecture called the exchanged generalized hypercube (EGH). We study the properties of EGH, such as the number of edges, the degree of vertices, connectivity, diameter, and diagnosability. Then, we give a routing algorithm to find the shortest path between any two distinct vertices of EGH. Furthermore, we design an algorithm to give disjoint paths between any two distinct vertices of EGH. In addition, we propose two local diagnosis algorithms: LDT $_{EGH}$ E G H and LDWB $_{EGH}$ E G H in EGH under PMC model and MM model, respectively. Simulation results demonstrate that even if the proportion of faulty vertices in EGH is up to 25 percent, the probability that these two diagnosis algorithms can successfully determine the status of vertices is more than 90 percent. As far as the number of edges is concerned, the analysis shows that the construction cost of EGH is much less than that of GH. We could regard this work as the basis for proposing future new high performance topologies.

Induced H-Packing k-Partition Problem in Certain Networks

A collection = {H1,H2,..., Hr } of induced sub graphs of a graph G is said to be sg-independent if (i) V(Hi) V(Hj )= , i j, 1≤ i, j≤ r and (ii) no edge of G has its one end in Hi and the other end in Hj , i j, 1≤ i, j≤ r. If Hi H, ∀ i, 1≤ i ≤r, then is referred to as a H-independent set of G. Let be a perfect or almost perfect H-packing of a graph G. Finding a partition of such that is H-independent set, ∀ i, 1 ≤ i ≤ k, with minimum k is called the induced H-packing k-partition problem of G. The induced H-packing k-partition number denoted by ipp(G,H) is defined as ipp(G,H) = min (G,H) where the minimum is taken over all H-packing of G. In this paper we obtain the induced H-packing k-partition number for Enhanced hypercube, Augmented Cubes and Crossed Cube networks where H is isomorphic to and .

All-Optical DFT Using TOAD-Based Cross-Bar Switches

The discovery of ultra-high-speed all-optical switches in the very recent past based on semiconductor optical amplifier (SOA) especially in the interferometric configuration is very pronouncing due to their features like high repetition rate, low power consumption, fast switching time, noise and jitter tolerance, being easily integrable and operationally versatile, thereby bringing a revolution in all-optical information processing systems. In this work, an all-optical computing tool namely SOA-based [Formula: see text] terahertz optical asymmetric demultiplexer (TOAD) is used because it can be employed to design more complex circuits and subsystems of enhanced combinational and sequential functionality. In this paper, (a) a switching network with its two switching actions and (b) an all-optical [Formula: see text] cross-bar network architecture, i.e., a multistage cube network for [Formula: see text] using TOAD-based [Formula: see text] optical cross-bar switch for discrete Fourier transform (DFT), are proposed. Numerical simulation of this work is done with OptiSystem v7.0 to evaluate the performance of the proposed circuit.