Hierarchical Interconnection Network Research Articles

Synthesis and Characterization of Ni–Co–O Nanosheets on Silicon Carbide Microspheres/Graphite Composite for Supercapacitor Applications

The well-interconnected ternary Ni–Co–O nanosheets were grown on silicon carbide microspheres/graphite composite (gra@SiC/Ni–Co–O) by optimizing the electrodeposition method. Silicon carbide microspheres/graphite composite (gra@SiC) serves as a conductive template for the growth of Ni–Co–O nanosheets to form a binder-free 3D well-designed hierarchical interconnected network between the Ni–Co–O nanosheets and SiC microspheres. The obtained gra@SiC/Ni–Co–O is proposed as a great capacitance performance for supercapacitors. Field emission scanning electron microscopy (FESEM), Raman spectroscopy, high-resolution transmission electron microscopy (HRTEM) with selected area electron diffraction (SAED) and energy dispersive X-ray spectroscopy (EDS), X-ray photoelectron spectroscopy, and electrochemical analysis were employed to investigate the morphology and structural and electrochemical characteristics. The synergistic effects of EDLC (SiC microspheres) and pseudo-capacitance (Ni–Co–O nanosheets) can effectively improve the supercapacitive performance. It is also worth mentioning that after electrochemical testing, the redox reaction of Ni–Co–O nanosheets greatly promoted the faradic pseudo-capacitance contribution, and silicon carbide microspheres/graphite composite contributed to the formation of a 3D interconnected network, improving the cycling stability during the charging/discharging processes.

Torus-Connected Toroids: An Efficient Topology for Interconnection Networks

Recent supercomputers embody hundreds of thousands of compute nodes, and sometimes millions; as such, they are massively parallel systems. Node interconnection is thus critical to maximise the computing performance, and the torus topology has come out as a popular solution to this crucial issue. This is the case, for example, for the interconnection network of the Fujitsu Fugaku, which was ranked world no. 1 until May 2022 and is the world no. 2 at the time of the writing of this article. Here, the number of dimensions used by the network topology of such torus-based interconnects stays rather low: it is equal to three for the Fujitsu Fugaku’s interconnect. As a result, it is necessary to greatly increase the arity of the underlying torus topology to be able to connect the numerous compute nodes involved, and this is eventually at the cost of a higher network diameter. Aiming at avoiding such a dramatic diameter rise, topologies can also combine several layers: such interconnects are called hierarchical interconnection networks (HIN). We propose, in this paper, which extends an earlier study, a novel interconnect topology for massively parallel systems, torus-connected toroids (TCT), whose advantage compared to existing topologies is that while it retains the torus topology for its desirable properties, the TCT network topology combines it with an additional layer, toroids, in order to significantly lower the network diameter. We both theoretically and empirically evaluate our proposal and quantitatively compare it to conventional approaches, which the TCT topology is shown to supersede.

The Morphology-Controllable Synthesis of Ni–Co–O Nanosheets on a 3D Porous Ni Template as a Binder-Free Electrode for a Solid-State Symmetric Supercapacitor

In this work, a porous Ni template (Ni–Co–O@3D Ni) with Ni–Co oxide nanosheets (Ni–Co–O)@3D was synthesized by incorporating Ni–Co oxide nanosheets within a 3D porous Ni template as a binder-free electrode for a supercapacitor. The 3D Ni template was synthesized with hydrogen bubble templates that possessed different applied voltages that marked differences in terms of physicochemical properties, as well as factors that affect the subsequent growth of Ni–Co–O nanosheets. Then, Ni and Co metal ion sources were introduced to produce the morphology adjustment of Ni–Co–O@3D Ni with a multiple hierarchical architecture with a hydrothermal process. Field emission scanning electron microscopy (FESEM), X-ray absorption spectroscopy (XAS), and an electrochemical analysis were employed to investigate the morphological, structural, and electrochemical characteristics. FESEM and XAS results evidenced that Ni–Co–O@3D Ni consists of a 3D, well-designed hierarchical interconnected network, and the local electronic structure change has a great influence on the capacitive performance. The electrochemical results of Ni–Co–O@3D Ni displayed an excellent electrochemical performance due to the synergistic effect of Ni and Co on Ni–Co–O@3D Ni, which possessed multiple oxidation states to enable various reversible Faradaic redox reactions. Remarkably, the solid-state symmetric supercapacitor fabricated with Ni–Co–O@3D Ni exhibited excellent capacitive behaviour at a wide operating voltage window and cycling performance. Also, the as-assembled solid-state symmetric supercapacitor (two devices in series) can successfully illuminate a desired parallel pattern consisting of 36 red LED lights, demonstrating its practical application as a supercapacitor.

Ordered mesoporous carbon with hierarchical pore structure for high-efficiency electromagnetic wave absorber under thin matching thickness

An enormous challenge exists in the development of low-density and efficient microwave absorbers with thin matching thickness. Carbon materials with hierarchical porosity are regarded as potential candidates for practical applications of microwave absorption (MA) materials on account of their rich pore structure which facilitates the entry and attenuation of electromagnetic waves. Herein, ordered mesoporous carbon with hierarchical interconnected network structure (NOMC) was prepared through a self-assembly method and calcination treatment. It was found that by adjusting the annealing temperature, the hierarchical porous structure, the carbon defect, the dielectric loss property and the MA property could be tuned. Thanks to the balance between sufficient hierarchical porous structure, outstanding impedance matching condition and multiple loss modes, NOMC displays outstanding ability to dissipate electromagnetic waves at a very thin absorbing coating thickness. Notably, as-prepared NOMC-700 displays an outstanding MA property, whose minimum reflection loss (RLmin) value reaches −27.5 dB at 16.72 GHz and the effective absorption bandwidth (EAB) achieves 3.2 GHz (14.8–18 GHz) under 1.5 mm absorbing coatings. Hence, the satisfying design in porous microstructure can pave the way for efficient MA materials with thin matching thickness.

Static Evaluation of a Midimew Connected Torus Network for Next Generation Supercomputers

Many artificially intelligent systems solve complex health- and agriculture-related problems that require great computational power. Such systems are used for tracking medical records, genome sequence analysis, image-based plant disease detection, food supply chain traceability, and photosynthesis simulation. Massively parallel computers (MPCs) are among those used to solve these computation-intensive problems. MPCs comprise a million nodes; connecting such a large number of nodes is a daunting task. Therefore, hierarchical interconnection networks (HINs) have been introduced to solve this problem. A midimew-connected torus network (MTN) is a HIN that has basic modules (BM) as torus networks that are connected hierarchically by midimew links. This paper presents the performance of MTNs in terms of static topological parameters and cost-effectiveness, as measured through simulations. An MTN was compared with other networks, including mesh, torus, TESH, TTN, MMN, and TFBN. The results showed that our MTN had a low diameter with a high bisection width and arc connectivity. In addition, our MTN had a high cost–performance trade-off factor (CPTF), a high cost-effective factor (CEF), low packing density, and moderate message-traffic density with marginally higher costs, as compared to other networks, due to wire complexity. However, our MTN provided better bandwidth with higher static fault tolerance. Therefore, MTNs are suggested for further evaluation of the effective implementation of MPCs.

Double ion-buffering reservoirs of advanced NiCo//G-PANI asymmetric supercapacitors with high performance

Asymmetric supercapacitors (ASCs) have been designed due to their lower cost effectiveness, better safety, long cycle life, and high energy/power density. Herein, the ASC of double “ion-buffering reservoirs” NiCo2O4-CNT-c-PEGm//rGO-PANI (NiCo//G-PANI) with high capacity and ultralong lifetime were fabricated and evaluated. The three-dimensional hierarchical flower-like NiCo2O4-CNT-c-PEGm microspheres were prepared via solvothermal method. In these composites, the incorporated CNTs were modified with methoxypolyethylene glycol (mPEG) polymer by Cu(I)-catalyzed click chemistry. The NiCo2O4-CNT-c-PEGm composites with typical honeycomb-like “ion-buffering reservoir” structures exhibited the specific capacity of 191.3 mAh g−1 at 0.5 A g−1. Moreover, the rGO-PANI composites with hierarchical interconnected porous network structures as “ion-buffering reservoir” were prepared via in situ polymerization and chemical reduction. Further, the rGO-PANI electrode materials could achieve the specific capacity of 81.5 mAh g−1 at 1 A g−1. Owing to such excellent attributes, the as-assembled ASC NiCo//G-PANI exhibit the specific capacity of 84.7 mAh g−1 at 1 A g−1 and high energy density of 67.7 Wh Kg−1 at a power density of 800 W Kg−1 for the potential applications in electric energy storage technologies. As a result, this study promotes an innovative strategy to synthesize the metal oxides modified with carbon materials as positive electrode materials to assemble the new type of ASCs.

HFBN: An Energy Efficient High Performance Hierarchical Interconnection Network for Exascale Supercomputer

Supercomputers are trying to be eco-friendly using their main components like- interconnection networks, processors, and shared memory through high power efficiency (GFlops/watts). The reason for this is the exascale systems, are on the horizon, require a 1000 times performance improvement over the petascale computers and energy efficiency has attracted as the key factor for to achieve exascale system. The main contribution of this paper is to introduce a new hierarchical interconnection network; considering simulations at the million processing cores especially for the exascale system. Moreover, our designed network claims the supremacy of high network performance and low power consumption over the conventional networks and ensuring the utmost preferability for exaFLOPS system. On the other hand, the performance per watt metric, used for the TOP500 list, doesn’t reflect the overall performance of a given system. Hence, one of the possible solutions to reach the next generation exascale performance is to redesign the "Interconnection Network", which holds the main responsibility for the intercommunication between the CPUs and also the power consumption for the supercomputers. This paper focuses on a redesigned new energy efficient interconnection network that mitigates the problems of high power consumption, longer wiring length, and low bandwidth issues. Our designed network (HFBN) has been compared against the Tofu network and in the case of 1M cores, HFBN can obtain about 87.26% better energy efficiency at the zero load latency with uniform traffic, about 86.32% with perfect shuffle traffic, and about 92.98% with the bit-compliment traffic.

A Novel Tradeoff Analysis between Traffic Congestion and Packing Density of Interconnection Networks for Massively Parallel Computers

From disaster prevention to mitigation, drug analysis to drug design, agriculture to food security, IoT to AI, and big data analysis to knowledge or sentiment mining, a high computation power is a prime necessity at present. As such, massively parallel computer (MPC) systems comprising a large number of nodes are gaining popularity. To interconnect these huge numbers of nodes efficiently, hierarchical interconnection networks are an attractive and feasible option. A Tori-connected flattened butterfly network (TFBN) has been proposed by the authors in a prior work for future generation MPC systems. In the previous study, the static network performance and static cost-effectiveness were evaluated. In this research, a novel trade-off factor named message traffic congestion vs. packing density trade-off factor has been proposed, which characterizes the message congestion in the network and its packing density. The factor is used to statically assess the suitability of the implementation of an interconnection network. The message traffic density, packing density, and new factor have been evaluated for the proposed network and similar competitive networks such as TTN, TESH, 2D-Mesh, 3D-Mesh, 2D-Torus, and 3D-Torus. It has been found that the performance of the TFBN is superior to the other networks.

3D-TTN: a power efficient cost effective high performance hierarchical interconnection network for next generation green supercomputer.

Green computing is an important factor to ensure the eco-friendly use of computers and their resources. Electric power used in a computer converts into heat and thus, the system takes fewer watts ensuring less cooling. This lower energy consumption allows to be less costly to run as well as reduces the environmental impact of powering the computer. One of the most challenging problems for the modern green supercomputers is the reduction of current power consumptions. Consequently, regular conventional interconnection networks also show poor cost performance. On the other hand, hierarchical interconnection networks (like-3D-TTN) can be a possible solution to those issues. The main focus for this paper is the estimation of power usage at the on-chip level for 3D-TTN with the various other networks along with the analysis of static network performance. In our analysis, 3D-TTN requires about 32.48% less router power usage at the on-chip level and can also achieve near about 21% better diameter performance as well as 12% better average distance performance than the 5D-Torus network. Similarly, it also requires only about 14.43% higher router power usage; however, can achieve 23.21% better diameter performance and 26.3% better average distance than recent hierarchical interconnection network- 3D-TESH. The most attractive feature of this paper is the static hop distance parameter and per watt analysis (power-performance). According to our power-performance results, 3D-TTN can also show better result than the 3D-Mesh, 2D-Mesh, 2D-Torus and 3D-TESH network even at the lowest network level. Moreover, this paper is also featured with the static effectiveness analysis, which ensures cost and time efficiency of 3D-TTN.

TFBN: A Cost Effective High Performance Hierarchical Interconnection Network

In order to fulfill the increasing demand for computation power to process a boundless data concurrently within a very short time or real-time in many areas such as IoT, AI, machine learning, smart grid, and big data analytics, we need exa-scale or zetta-scale computation in the near future. Thus, to have this level of computation, we need a massively parallel computer (MPC) system that shall consist of millions of nodes; and, for the interconnection of these massive numbers of nodes, conventional topologies are infeasible. Thus, a hierarchical interconnection network (HIN) is a rational way to connect huge nodes. Through this article, we are proposing a new HIN, which is a tori-connected flattened butterfly network (TFBN) for the next generation MPC system. Numerous basic modules are hierarchically interconnected as a toroidal connection, whereby the basic modules are flattened butterfly networks. We have studied the network architecture, static network performance, and static cost-effectiveness of the proposed TFBN in detail; and compared static network and cost-effectiveness performance of the TFBN to those of TTN, torus, TESH, and mesh networks. It is depicted that TFBN possesses low diameter and average distance, high arc connectivity, and temperate bisection width. It also has better cost-effectiveness and cost-performance trade-off factor compared to those of TTN, torus, TESH, and mesh networks. The only shortcoming is that the complexity of wiring of the TFBN is higher than that of those networks; this is because the basic module necessitates some extra short length link to form the flattened butterfly network. Therefore, TFBN is a high performance and cost-effective HIN, and it will be a good option for the next generation MPC system.

Facilitated self-assembly of a prevascularized dermal/epidermal collagen scaffold.

Introduction: Resurfacing complex full thickness wounds requires free tissue transferwhich creates donor site morbidity. We describe a method to fabricate a skin flap equivalent with a hierarchical microvascular network. Materials & methods: We fabricated a flap of skin-like tissue containing a hierarchical vascular network by sacrificing Pluronic® F127 macrofibers and interwoven microfibers within collagen encapsulating human pericytes and fibroblasts. Channels were seeded with smooth muscle and endothelial cells. Constructs were topically seeded with keratinocytes. Results: After 28days in culture, multiphoton microscopyrevealed a hierarchical interconnected network ofmacro- and micro-vessels; larger vessels (>100μm) were lined with a monolayer endothelial neointima and a subendothelial smooth muscle neomedia. Neoangiogenic sprouts formed in the collagen protodermis and pericytes self-assembled around both fabricated vessels and neoangiogenic sprouts. Conclusion: We fabricated a prevascularized scaffold containing a hierarchical 3Dnetwork of interconnected macro- and microchannels within a collagen protodermis subjacent to an overlying protoepidermis with the potential for recipient microvascular anastomosis.

SCCN: A Time-Effective Hierarchical Interconnection Network for Network-On-Chip

The needed time to send and receive a message among two nodes in an interconnection network has a fundamental role in determining the performance of this network. Therefore, taking a short period of time to send a packet between a source and destination nodes indicates a good performance network with less congestion and latency. Besides, processing data in short-term help in providing fast solutions for many complex problems. Thus, various designs of hierarchical interconnection networks (HINs) for the massively parallel computer (MPC) systems have been presented recently; the main goal of these networks is to replace the conventional ones which showed poor performance in scaling the network size. A Shifted Completely Connected Network (SCCN) proposed as a new HIN topology. Several basic modules (BMs) interconnected hierarchically to create advanced levels networks based on this topology. The structural design and a proposed routing protocol of SCCN discussed in this paper. However, the foremost focus of this work is to evaluate the time cost-effectiveness factor (TCEF) of SCCN in different levels in order to examine the effect of expanding the size of the network on the TCEF. Therefore, the TCEF for the higher levels of SCCN from level (1) to level (3) will be assessed to examine whether SCCN is an effective network in term of time. In addition, the obtained results from each level will be compared to other networks to prove the preeminence of the proposed topology.

Bimodal nanoporous Pd3Cu1 alloy with restrained hydrogen evolution for stable and high yield electrochemical nitrogen reduction

Electrocatalytic nitrogen reduction reaction (NRR) under ambient temperature and pressure holds a great promise for NH3 production while it is still impeded by the low active site density and sluggish kinetics, leading to a low product yield rate. In this work, bimodal nanoporous PdCu alloys that have three-dimensional hierarchical interconnected porous network and tailored Pd/Cu atomic ratios are designed and used for electrocatalytic NRR with high NH3 yield rate at room temperature and atmosphere pressure. The Pd3Cu1 alloy that has large surface area for high active site density, bimodal porous structure for efficient reactant accessibility as well as desired electronic structure for restrained hydrogen evolution reaction exhibits a high NH3 yield rate of 39.9 μg h−1 mgcat−1, which is among the highest values for recently reported NRR electrocatalysts with high loading amount. Even at a low overpotential of − 0.15 V versus reversible hydrogen electrode (vs RHE), the alloy can still deliver a NRR yield rate of more than 10 μg h−1 mgcat−1. Moreover, structural integrity of the Pd3Cu1 alloy makes it a highly stable NRR electrocatalyst that keeps 100% of its original activity after 18 h operation, retaining its great potential for promising NRR electrocatalysis. The synergistic combination of bimodal nanoporous structure and alloy strategy could be used to design efficient catalysts for a wide range of reactions.

Alginic acid-derived mesoporous carbonaceous materials (Starbon®) as negative electrodes for lithium ion batteries: Importance of porosity and electronic conductivity

Alginic acid-derived mesoporous carbonaceous materials (Starbon® A800 series) were investigated as negative electrodes for lithium ion batteries. To this extent, a set of mesoporous carbons with different pore volume and electronic conductivity was tested. The best electrochemical performance was obtained for A800 with High Pore Volume (A800HPV), which displays both the highest pore volume (0.9 cm3 g−1) and the highest electronic conductivity (84 S m−1) of the tested materials. When compared to a commercial mesoporous carbon, A800HPV was found to exhibit both better long-term stability, and a markedly improved rate capability. The presence of a hierarchical interconnected pore network in A800HPV, accounting for a high electrolyte accessibility, could lay at the origin of the good electrochemical performance. Overall, the electronic conductivity and the mesopore size appear to be the most important parameters, much more than the specific surface area. Finally, A800HPV electrodes display similar electrochemical performance when formulated with or without added conductive additive, which could make for a simpler and more eco-friendly electrode processing.

Modular ceramic scaffolds for individual implants

Ideal artificial bone grafts aim for multiscale porosity, high mechanical strength and ensure rapid vascularization for bone ingrowth. In this work modular ceramic arteriovenous loops (AV-loops) with a hierarchical porosity approach were designed and manufactured to meet these criteria and to exceed the poor mechanical strength of monolithic scaffolds. Bioactive building blocks (β-TCP, HAp, BCP) with dimensions of 1.5–3.0 mm were prepared by injection molding and assembled to complex AV-loop scaffolds using a customized automated assembly technology (pick and place). The building blocks were bonded with a biocompatible adhesive. Single building blocks are characterized by a compressive strength of 112.4–134.5 MPa with a residual sintering porosity of 32.2–41.5%, matching the strength of cortical bone of 100–230 MPa. The compressive strength of the modular assemblies varied between 22.3 and 47.6 MPa primary depending on the building block arrangement. The achieved compressive strengths are superior to current monolithic AV-scaffolds and sufficient for the implantation as non-load-bearing AV-loop scaffolds in isolation chambers. The modular AV-loop scaffolds provide a hierarchical interconnected pore network (P = 58.8%) combining small macropores of 4.1–4.3 µm size for possible enhanced protein absorption and large gradient macropores of 200–1700 µm size for optimum vascularization and complete bone ingrowth. The modular building block approach allows to design patient individualized scaffolds with complex hierarchical pore networks. The pore volume, size and geometry as well as the biological response can effectively be tuned by changing the dimensions, shape and placing gap of the bioactive building blocks. Statement of SignificanceGold standard of bone replacement in case of surgery or cancer is still own bone material usually taken from the hip/arm or leg in second surgery with poor mechanical properties and limited amount. To avoid a second surgery and provide mechanical strong scaffold structures for fast patient regeneration a novel modular building block approach is used. This allows complex scaffold geometry with a hierarchical interconnection porosity for blood vessel ingrowth. The pore volume, size and geometry as well as the biological response can effectively be tuned by changing the dimensions, shape and placing gap of the bioactive building blocks.

2D metal–organic-framework array-derived hierarchical network architecture of cobalt oxide flakes with tunable oxygen vacancies towards efficient oxygen evolution reaction

The development of highly active dual-functional electrocatalysts, especially for oxygen evolution reaction (OER), is highly desirable to electrocatalyze water splitting for hydrogen production. Herein, a cobalt metal-organic frameworks (Co-MOFs) array is employed as the platform to fabricate oxygen-defect-rich Co3O4 flakes that are vertical grown on nickel foam substrates. This MOFs-derived Co3O4 arrays show a hierarchical interconnected porous flake network structure with tunable oxygen vacancies. The unique structural features obtained from an optimal hydrogenation condition render outstanding catalytic performance toward the oxygen evolution in alkaline media (an ultralow overpotential of 205 mV at 10 mA cm−2; a small Tafel slope of 65.3 mV dec−1 as well as high stability). This OER performance is among the best non-noble metal catalysts reported to date. Meanwhile, this defect-rich Co3O4 array electrode is also efficient for catalyzing hydrogen evolution in the same basic solution (overpotential of ∼108 mV at 10 mA cm−2). The electrolyzer for overall water splitting can deliver a current density of 100 mA cm−2 at a cell voltage as low as 1.84 V. Density functional theory calculation reveals that the enhanced OER performance mainly arises from the oxygen vacancies and consequently the lowered activation energy as well as improved electrical conductivity.

Three-Dimensional Hierarchical Architecture of the TiO2/Ti3C2Tx/RGO Ternary Composite Aerogel for Enhanced Electromagnetic Wave Absorption

Tunable and high-efficiency electromagnetic wave (EMW) absorption materials composed of a three-dimensional (3D) hierarchical reduced graphene oxide (RGO) aerogel network entrapped with TiO2/Ti3C2Tx hybrids were fabricated by a hydrothermal method and a mild chemical reduction treatment. The incorporation of the TiO2/Ti3C2Tx micronanoheterostructure and construction of the 3D well-designed hierarchical interconnected network can significantly reduce the agglomeration of RGO sheets together with the beneficial effect of a better impedance match. When the filler loading is 10 wt %, the maximum reflection loss of the composite aerogel reaches up to −65.3 dB with a matching thickness of 2.5 mm. Meanwhile, the effective absorption bandwidth (RL < −10 dB) is 4.3 GHz with the coating thickness of only 2.0 mm, and the tunable absorption bandwidth achieves at 13.74 GHz via modulating the absorber thicknesses in a range from 1.5 to 5.0 mm. The enhanced EMW absorbing performance is closely related to highly porous c...

An Optimum Value of Dynamic Communication Performance for Midimew Connected Mesh Network

A Midimew connected Mesh Network (MMN) is a proposed hierarchical interconnection network in which numerous basic modules are interconnected in a hierarchical fashion to construct a massively parallel computer. Here, the basic module is the first level of the network which is connected by mesh network while higher level network is connected by a midimew network. In this study, we have evaluated a dynamic communication performance of a variety of MMN using the TOPAZ simulator using a deadlock free routing algorithm with uniform traffic patterns, whereby the dimension order routing and virtual cut-through flow control are used. It is found that the saturation throughput of the Virtual MMN (VMMN) is higher than that of Horizontal MMN (HMMN), Symmetric MMN (SMMN), and Tori connected mESH network (TESH).

On topological properties of hierarchical interconnection networks

There is really a lot of mathematics involved in electrical and electronic engineering. It depends on what area of electrical and electronic engineering, for example there is a lot more abstract mathematics in communication theory and signal processing and networking etc. Networks involve nodes communicating with each other. A lot of computers linked together form a network. Cell phone users form a network. Networking involves the study of the best way of implementing a network. Graph theory has found a considerable use in this area of research. In this paper, we extend this study to interconnection networks and derive analytical closed results of general Randic index $$R_{\alpha }(G)$$ for different values of “ $$\alpha $$ ” for block shift network (BSN-1) and (BSN-2), Hierarchical hypercube (HHC-1) and (HHC-2). We also compute first Zagreb, $$\textit{ABC}$$ , $$\textit{GA}$$ , $$\textit{ABC}_{4}$$ and $$\textit{GA}_{5}$$ indices and give closed formulae of these indices for Hierarchical interconnection networks.

Torus–Connected Cycles: A Simple and Scalable Topology for Interconnection Networks

Abstract Supercomputers are today made up of hundreds of thousands of nodes. The interconnection network is responsible for connecting all these nodes to each other. Different interconnection networks have been proposed; high performance topologies have been introduced as a replacement for the conventional topologies of recent decades. A high order, a low degree and a small diameter are the usual properties aimed for by such topologies. However, this is not sufficient to lead to actual hardware implementations. Network scalability and topology simplicity are two critical parameters, and they are two of the reasons why modern supercomputers are often based on torus interconnection networks (e.g., Fujitsu K, IBM Sequoia). In this paper we first describe a new topology, torus-connected cycles (TCCs), realizing a combination of a torus and a ring, thus retaining interesting properties of torus networks in addition to those of hierarchical interconnection networks (HINs). Then, we formally establish the diameter of a TCC, and deduce a point-to-point routing algorithm. Next, we propose routing algorithms solving the Hamiltonian cycle problem, and, in a two dimensional TCC, the Hamiltonian path one. Correctness and complexities are formally proved. The proposed algorithms are time-optimal.