Interconnection Network Topology Research Articles

Hierarchical Hexagon: A New Fault-Tolerant Interconnection Network for Parallel Systems

Abstract A new interconnection network topology called Hierarchical Hexagon HH(n) is proposed for massively parallel systems. The new network uses a hexagon as the primary building block and grows hierarchically. Our proposed network is shown to be superior to the star based and the hypercube networks, with respect to node degree, diameter, network cost, and fault tolerance. We thoroughly analyze different topological parameters of the proposed topology including fault tolerance routing and embedding Hamiltonian cycle.

The Static Performance Effect of Hybrid- Hierarchical Interconnection by Shifted Completely Connected Network

Massively parallel computer (MPC) systems execute many operations based on internal networks called interconnection networks. The performance of these networks is affected by their topologies.There are many topologies of interconnection networks for MPC systems, unfortunately, they faced many drawbacks. Expanding the size of the network degrades the performance of these topologies. That is why this current paper presents a hybrid-hierarchical interconnection network (HIN) topology by Shifted Completely Connected Network (SCCN) to circumvent the drawbacks of the existing topologies. An experimental evaluation involving the design and development of a hierarchical network was carried out. A two-dimensional higher level networks has been produced and its static network performance parameters evaluated through simulators. The finding of the simulations has shown some good performances compared to many previous designed networks. SCCN is better than all conventional networks in terms of diameter, cost and average distance.

Leafycube: A Scalable and Load Balanced Interconnection Network Topology

Leafycube: A Scalable and Load Balanced Interconnection Network Topology

The Irregularity Polynomials of Fibonacci and Lucas cubes

Irregularity of a graph is an invariant measuring how much the graph differs from a regular graph. Albertson index is one measure of irregularity, defined as the sum of $$|deg(u)-deg(v)|$$ over all edges uv of the graph. Motivated by a recent result on the irregularity of Fibonacci cubes, we consider irregularity polynomials and determine them for Fibonacci and Lucas cubes. These are graph families that have been studied as alternatives for the classical hypercube topology for interconnection networks. The irregularity polynomials specialize to the Albertson index and also provide additional information about the higher moments of $$|deg(u)-deg(v)|$$ in these families of graphs.

When Are Cyber Blackouts in Modern Service Networks Likely?

Service liability interconnections among globally networked IT- and IoT-driven service organizations create potential channels for cascading service disruptions worth billions of dollars, due to modern cyber-crimes such as DDoS, APT, and ransomware attacks. A natural question that arises in this context is: What is the likelihood of a cyber-blackout? , where the latter term is defined as the probability that all (or a major subset of) organizations in a service chain become dysfunctional in a certain manner due to a cyber-attack at some or all points in the chain. The answer to this question has major implications to risk management businesses such as cyber-insurance when it comes to designing policies by risk-averse insurers for providing coverage to clients in the aftermath of such catastrophic network events. In this article, we investigate this question in general as a function of service chain networks and different cyber-loss distribution types. We show somewhat surprisingly (and discuss the potential practical implications) that, following a cyber-attack, the effect of (a) a network interconnection topology and (b) a wide range of loss distributions on the probability of a cyber-blackout and the increase in total service-related monetary losses across all organizations are mostly very small. The primary rationale behind these results are attributed to degrees of heterogeneity in the revenue base among organizations and the Increasing Failure Rate property of popular (i.i.d/non-i.i.d) loss distributions, i.e., log-concave cyber-loss distributions. The result will enable risk-averse cyber-risk managers to safely infer the impact of cyber-attacks in a worst-case network and distribution oblivious setting.

Research on Topoloty Reconstruction Mechanism Based on Traffic Identification

<p align="justify">Due to the growing variety of data center services, the bursty and variability of data traffic is increasing. In order to make the network better meet the needs of upper-layer services, it is necessary to design a more flexible optical internet topology reconstruction mechanisms to adapt the changing traffic demands. In the past research on optical internet, all topology reconstruction mechanisms are designed based on global data traffic. Although these mechanisms can fully utilize the flexibility of the data center optical interconnection network topology and adjust topology in real time according to the traffic demands, but when the traffic is presented at the regional level, this mechanism does not give optimal results. This paper proposes a topology reconstruction mechanism for data center optical interconnection network based on traffic identification for the previously proposed data center optical switching architecture—OpenScale. The simulation results show that it utilizes the flexibility of the network to save bandwidth resources and increase the wavelength connection bandwidth utilization with a little sacrifice of throughput.</p>

Constructing dual-CISTs of pancake graphs and performance assessment of protection routings on some Cayley networks

For a connected graph $$G=(V,E)$$ , two spanning trees $$T_1$$ and $$T_2$$ of G are said to be a pair of completely independent spanning trees (or a dual-CIST for short) if for any two vertices $$u,v\in V$$ , the paths joining u and v in the two trees have no common vertex except for u and v. Although the existence of a dual-CIST in the underlying graph of a network has the practical application of protection routing on fault-tolerance, it has been proved that determining whether a graph G admits a dual-CIST is NP-complete. As we know that Cayley graphs are a large family of graphs, some of its subclasses have been attracted and thus graphs in these subclasses have been adopted as the topologies of interconnection networks, such as the n-dimensional star graphs $$S_n$$ , bubble sort graphs $$BS_n$$ , pancake graph $$P_n$$ , alternating group networks $$AGN_n$$ and so on. Pai and Chang (IEEE/ACM Trans Netw 27(3): 1112–1123, 2019) recently showed that there exist dual-CISTs in $$S_n$$ , $$BS_n$$ , $$AGN_n$$ for $$n\geqslant 5$$ and provided their corresponding protection routings. So far, the problem of constructing dual-CISTs on $$P_n$$ has not been dealt with yet. In this sequel, we continue the investigation of the construction of dual-CISTs in pancake graphs as a complementary result. Since $$P_n$$ , $$S_n$$ , and $$BS_n$$ are with the same scale, we experimentally assess the performance of protection routing through simulation results for comparing them when $$n=5,6,7$$ .

On Component Connectivity of Hierarchical Star Networks

For an integer [Formula: see text], the [Formula: see text]-component connectivity of a graph [Formula: see text], denoted by [Formula: see text], is the minimum number of vertices whose removal from [Formula: see text] results in a disconnected graph with at least [Formula: see text] components or a graph with fewer than [Formula: see text] vertices. This naturally generalizes the classical connectivity of graphs defined in term of the minimum vertex-cut. This kind of connectivity can help us to measure the robustness of the graph corresponding to a network. The hierarchical star networks [Formula: see text], proposed by Shi and Srimani, is a new level interconnection network topology, and uses the star graphs as building blocks. In this paper, by exploring the combinatorial properties and fault-tolerance of [Formula: see text], we study the [Formula: see text]-component connectivity of hierarchical star networks [Formula: see text]. We obtain the results: [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text].

Leader-following Consensus of Linear Fractional-order Multi-agent Systems via Event-triggered Control Strategy

Many complex systems can be more accurately described by fractional-order models. In this paper, a leader-following consensus problem of fractional-order multi-agent systems (FOMASs) is firstly formulated and then an event-trigger consensus control is proposed for each agent. Under the assumption that the interconnection network topology has a spanning tree, consensus of the closed-loop FOMAS is analyzed with the help of the Mittag-Leffler functions and stability theory of fractional-order differential equations. It is shown that Zeno behavior can be avoided. Simulation results are presented to demonstrate the effectiveness of the theoretical results.

Reliable, Effective and Fault-Tolerant Design of LeafyCube Interconnection Network Topology

This paper attempts to derive the performance properties of the Leafycube (LC) interconnection network. The Leafycube is already observed to have quite superior topological properties in comparison to the other contemporary networks. The various performance parameters of the LC network are studied and compared with the existing HC and its variants. The routing and broadcasting algorithms are proposed and the time complexities are also compared. The paper attempts to evaluate the cost effectiveness, reliability and fault tolerance aspects of LC interconnection network in order to justify the novelty in the design of the proposed structure. The leafy structure helps to retain the original hypercube while improving the node packing density in the interconnection network.

Enhancement Replicated Network: A Reliable Multistage Interconnection Network Topology

Shuffle-exchange networks (SENs) have been generally considered to provide convenient interconnection systems due to the size of their switching elements and simple configuration. Notwithstanding the evaluation of the reliability performance of SENs attempted by researchers in the past, this paper provides an in-depth study. This paper proposes a new topology called the Replicated Enhanced Augmented SEN. This topology makes use of an Enhanced Augmented SEN by replicating the network to create a redundant path and increase the reliability performance. The reliable operation of interconnection networks is the main concern in system performance. Reliable operation in multistage interconnection networks depends on their topology, network configuration, and number of stages in the system. The terminal reliability analysis showed that the approach of using a replicated network resulted in the highest performance in terms of reliability.

A New Cost Effective and Reliable Interconnection Topology for Parallel Computing Systems

Topology of the of interconnection network is one of the most important considerations in the design of parallel systems as it is the backbone network over which the different components of the computer communicate with each other. The properties of the topology such as connectivity, reliability, cost, fault tolerance, diameter and bisection width determine the flawless-less data transmission between the source and the sink nodes. In this paper, we propose a new hybrid interconnection network topology called TOR-CUBE (TC) which is a product of two classical popular interconnection topologies namely hypercube and torus. Further, we show the construction and characteristics of the proposed interconnection topology. We also presented some basic important properties and formulated two routing algorithms for TC. Our results show that the proposed interconnection topology has high connectivity, lesser diameter, low cost, fault tolerant, scalable and low average distance. The different reliability measures of TC are computed and found to be better as compared with its counterpart topologies and the parent topologies.

Subnetwork reliability analysis in [formula omitted]-ary [formula omitted]-cubes

The k-ary n-cube is one of the most attractive interconnection network topologies for parallel computing systems. In this paper, we derive an upper bound on the k-ary (n−1)-cube reliability in a k-ary n-cube with odd k≥3 using the probability fault model. An approximate k-ary (n−1)-cube reliability result is also obtained using the fixed partitioning. The numerical results show that the k-ary (n−1)-cube reliabilities under the probability fault model and the fixed partitioning are in good agreement. The numerical results are also shown to be consistent with and close to the simulation results.

Amortized efficiency of constructing multiple independent spanning trees on bubble-sort networks

A set of spanning trees in a graph G is called independent spanning trees (ISTs for short) if they are rooted at the same vertex, say r, and for each vertex $$v(\ne r)$$ in G, the two paths from v to r in any two trees share no common edge and no common vertex except for v and r. Constructing ISTs has applications on fault-tolerant broadcasting and secure message distribution in reliable communication networks. Since Cayley graphs have been used extensively to design the topologies of interconnection networks, construction of ISTs on Cayley graphs is significative. It is well-known that star networks $$S_n$$ and bubble-sort network $$B_n$$ are two of the most attractive subclasses of Cayley graphs. Although it has been dealt with about two decades for the construction of ISTs on $$S_n$$ (which has been pointed out that there is a flaw and has been corrected recently), so far the problem of constructing ISTs on $$B_n$$ is not dealt with yet. In this paper, we present an algorithm to construct $$n-1$$ ISTs of $$B_n$$ . Moreover, we show that our algorithm has amortized efficiency for multiple trees construction. In particular, every vertex can determine its parent in each spanning tree in a constant amortized time. Accordingly, except for the star networks, it seems that our work is the latest breakthrough on the problem of ISTs for all subfamilies of Cayley graphs.

Optimally Embedding 3-Ary n-Cubes into Grids

The 3-ary n-cube, denoted as $$ {Q}_n^3 $$ , is an important interconnection network topology proposed for parallel computers, owing to its many desirable properties such as regular and symmetrical structure, and strong scalability, among others. In this paper, we first obtain an exact formula for the minimum wirelength to embed $$ {Q}_n^3 $$ into grids. We then propose a load balancing algorithm for embedding $$ {Q}_n^3 $$ into a square grid with minimum dilation and congestion. Finally, we derive an O(N2) algorithm for embedding $$ {Q}_n^3 $$ into a gird with balanced communication, where N is the number of nodes in $$ {Q}_n^3 $$ . Simulation experiments are performed to verify the total wirelength and evaluate the network cost of our proposed embedding algorithm.

Edge-Bipancyclicity of Bubble-Sort Star Graphs

The topology of interconnection networks determines the performance of the networks. Linear arrays and rings are two of the most fundamental structures of the interconnection network topologies owing to their simple structures and low degree. Thus how to embed cycles and paths into interconnection networks is a crucial factor for the networks. The interconnection network considered in this paper is the bubble-sort star graph. The n-dimensional bubble-sort star graph BS n is a bipartite and (2n - 3)-regular graph of order n!. A bipartite graph G of order IV(G)I is edge-bipancyclic if each edge of G lies on a cycle of all even length l with 4 ≤ l ≤ |V(G)|. In this paper, we show that the n-dimensional bubble-sort star graph BSn is edge-bipancyclic for n ≥ 3 and for each even length l with 4 ≤ l ≤ n!, every edge of BSn lies on at least four different cycles of length l. Moreover, we also have that BSn is vertex-bipancyclic and bipancyclic for n ≥ 3.

Paired many-to-many two-disjoint path cover of balanced hypercubes with faulty edges

As a variant of the well-known hypercube, the balanced hypercube $$BH_n$$ was proposed as a desired interconnection network topology for parallel computing. It is known that $$BH_n$$ is bipartite. Assume that $$S=\{s_1,s_2\}$$ and $$T=\{t_1,t_2\}$$ are any two sets of vertices in different partite sets of $$BH_n$$ ( $$n\ge 1$$ ). It has been proved that there exist two vertex-disjoint $$s_1,t_1$$ -path and $$s_2,t_2$$ -path of $$BH_n$$ covering all vertices of $$BH_n$$ . In this paper, we prove that there always exist two vertex-disjoint $$s_1,t_1$$ -path and $$s_2,t_2$$ -path covering all vertices of $$BH_n$$ ( $$n\ge 2$$ ) with at most $$2n-3$$ faulty edges. The upper bound $$2n-3$$ of edge faults can be tolerated is optimal.

Torus Pairwise Disjoint-Path Routing.

Modern supercomputers include hundreds of thousands of processors and they are thus massively parallel systems. The interconnection network of a system is in charge of mutually connecting these processors. Recently, the torus has become a very popular interconnection network topology. For example, the Fujitsu K, IBM Blue Gene/L, IBM Blue Gene/P, and Cray Titan supercomputers all rely on this topology. The pairwise disjoint-path routing problem in a torus network is addressed in this paper. This fundamental problem consists of the selection of mutually vertex disjoint paths between given vertex pairs. Proposing a solution to this problem has critical implications, such as increased system dependability and more efficient data transfers, and provides concrete implementation of green and sustainable computing as well as security, privacy, and trust, for instance, for the Internet of Things (IoT). Then, the correctness and complexities of the proposed routing algorithm are formally established. Precisely, in an n-dimensional k-ary torus (, ), the proposed algorithm connects c () vertex pairs with mutually vertex-disjoint paths of lengths at most , and the worst-case time complexity of the algorithm is . Finally, empirical evaluation of the proposed algorithm is conducted in order to inspect its practical behavior.

Utilization and Balance in Channel Assignment for Rural Wireless Mesh Networks

Wireless mesh networks with directional antennas are expected to be a new promising technology and an economic approach for providing wireless broadband services in rural areas. In these networks, the effective use of multiple non-overlapping channels can significantly enhance the network capacity by allowing more concurrent transmissions. However, the performances of wireless mesh networks are severely degraded by interference between links with overlapping channels in nearby areas. In this paper, we address the issue of joint utilization and balance in channel assignment for rural wireless mesh networks. We design a new channel assignment framework with the goal of optimizing the channel resource utilization across the entire network while taking balanced allocation into account. This balanced channel assignment allows for the cost-effective reuse of channels without a consequent loss of quality in the rural wireless mesh networks. We also evaluate the proposed framework on some Cartesian product graphs that are popular interconnection network topologies. The framework guarantees that these topologies require a small number of channels for balanced allocation.

Some diameter notions in lexicographic product of graphs

Many graphs such as hypercubes, star graphs, pancake graphs, grid, torus etc are known to be good interconnection network topologies. In any network topology, the vertices represent the processors and the edges represent links between the processors. Two most important criteria - efficiency and reliability of network models - can be studied with the help of graph theoretical techniques. The lexicographic product is a well studied graph product. The distance notions such as various diameters of a graph help to analyze the efficiency of any interconnection network. In this paper, we study some distance notions such as wide diameter, diameter variability and diameter vulnerability of lexicographic products that are useful in the design of interconnection networks.