Article
Mathematics, Applied
Dongqin Cheng
Summary: This paper investigates the restricted connectivity of n-dimensional balanced hypercubes and proves the minimum cardinality of the vertex set under certain conditions.
DISCRETE APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Ruichao Niu, Min Xu
Summary: The paper studies the fault-tolerant bipanconnectivity of bipartite n-dimensional hypercube-like networks and presents optimal results in terms of the number of faulty elements.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Computer Science, Theory & Methods
Huazhong Lu, Tingzeng Wu
Summary: This paper discusses the many-to-many k-disjoint path cover of a graph G and the balanced hypercube BHn, proving the existence of an unpaired many-to-many (2n-2)-disjoint path cover in BHn, while also improving existing results. The upper bound of 2n-2 is proven to be the best possible in terms of the number of disjoint paths in unpaired many-to-many k-DPC of BHn.
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
(2021)
Article
Computer Science, Theory & Methods
Yuxing Yang, Ningning Song
Summary: This article introduces the n-dimensional balanced hypercube BHn as a candidate interconnection network for multiprocessor systems, and proves that under certain conditions, BHn can achieve fault-free Hamiltonian paths between nodes.
THEORETICAL COMPUTER SCIENCE
(2023)
Article
Computer Science, Hardware & Architecture
Shiying Wang, Xiaolei Ma
Summary: This paper investigates the matching preclusion number and the strong matching preclusion number of the enhanced hypercube, providing specific values for each.
Article
Computer Science, Hardware & Architecture
Xinyang Wang, Lijuan Huang, Qiao Sun, Naqin Zhou, Yuehong Chen, Weiwei Lin, Keqin Li
Summary: This paper focuses on the g-extra diagnosability of the balanced hypercube, proving upper and lower bounds using the contradiction method and providing specific formulas under the PMC and MM* models. Simulation experiments were conducted to verify the effectiveness of the proposed theories, contributing certain theoretical and practical value to the research of BHn fault diagnosis.
JOURNAL OF SUPERCOMPUTING
(2022)
Article
Computer Science, Information Systems
Masaaki Okada, Keiichi Kaneko
Summary: The rapid growth in demand for high-performance computing has led to increased research on massively parallel systems. Interconnection networks play a crucial role in these systems, with the bicube topology gaining attention for its properties such as maintaining node symmetry and providing shorter path lengths compared to the popular hypercube topology. Researchers have focused on proposing algorithms to find the shortest path between nodes in the bicube topology and have demonstrated their correctness in execution.
IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS
(2022)
Article
Mathematics, Applied
Meijie Ma, Chaoming Guo, Xiang-Jun Li
Summary: The paper discusses the problem of embedding internally disjoint paths in an enhanced hypercube and proves that the subgraph obtained by deleting the faulty subnetwork from the enhanced hypercube remains strong Menger connected even when the network has faults.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Computer Science, Information Systems
Peng Zhou, Longxin Lin, Zhen Zhang, Yuhui Deng, Tengjiao He
Summary: Designing a cost-effective and energy-efficient data center network with sufficient bandwidth has gained significant attention. This paper proposes a new type of network structure called GHB, constructed using commercial switches and multi-port servers. The GHB structure shows comparable throughput and lower cost and energy consumption compared to existing structures such as BCube, DCell, and GBC3.
CLUSTER COMPUTING-THE JOURNAL OF NETWORKS SOFTWARE TOOLS AND APPLICATIONS
(2022)
Article
Computer Science, Hardware & Architecture
Lina Ba, Hailun Wu, Heping Zhang
Summary: This research explores the connectivity parameter of networks and introduces the concepts of structure connectivity and substructure connectivity of graphs. By computing the specific structure connectivity of n-dimensional folded hypercubes and augmented cubes, improved results are obtained compared to existing findings.
JOURNAL OF SUPERCOMPUTING
(2023)
Article
Computer Science, Hardware & Architecture
Peng Zhou, Longxin Lin, Tengjiao He, Zhen Zhang
Summary: As the volume of data continues to grow, the need for storage, management, and analysis in data center networks (DCNs) also increases. This paper proposes the GHDC (Generalized Hypercube Data Center) network structure, constructed using commodity switches and multi-port servers, which shows significant improvements in scalability, throughput, cost, and energy consumption compared to other DCN structures. The GHDC incorporates a routing algorithm that considers the shortest distance between any two vertices and introduces two incomplete GHDC structures for incremental scalability while maintaining topological properties. Overall, GHDC outperforms existing DCN structures and offers a cost-effective and energy-efficient solution.
JOURNAL OF SUPERCOMPUTING
(2023)
Article
Computer Science, Software Engineering
Yaodong Wang, Yamin Li
Summary: This paper proposes two hybrid topologies, CAT and MiCAT, based on fat-tree and hypercube, to reduce hardware costs in parallel supercomputers. The results show that CAT and MiCAT can save up to 87% switches and 80% links compared to fat-trees while maintaining higher path diversity.
CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE
(2023)
Article
Computer Science, Information Systems
Jung-Heum Park
Summary: This paper discusses the problem of finding disjoint paths in the underlying graph of an interconnection network in parallel processing. It reveals that constructing a nonbipartite torus-like graph with good disjoint-path-cover properties from lower dimensional torus-like graphs can retain the good property. Consequently, nonbipartite tori with at most f vertex and/or edge faults can have unpaired many-to-many disjoint path covers joining arbitrary disjoint sets.
Article
Computer Science, Artificial Intelligence
Xia Xiao, Jiaying Huang, Haobo Wang, Chengde Zhang, Xinzhong Chen
Summary: Paper recommendation based on author preferences has attracted significant attention. The proposed model utilizes open-metapaths to capture rich correlations between various type nodes in the heterogeneous information network (HIN), and outperforms existing models significantly.
EXPERT SYSTEMS WITH APPLICATIONS
(2023)
Article
Computer Science, Hardware & Architecture
Pranava K. Jha
Summary: This paper presents the properties of the quad-cube network, including vertex transitivity and an exact formula for the distance metric. The vertex distribution of the quad-cube resembles that of twin copies of a hypercube.
JOURNAL OF SUPERCOMPUTING
(2023)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)