Interconnection Network Topology Research Articles

Enhancing interconnection network topology for chiplet-based systems: An automated design framework

Chiplet-based systems integrate discrete chips on an interposer and use the interconnection network to enable communication between different components. The topology of the interconnection network poses a significant challenge to overall performance, as it can greatly affect both latency and throughput. However, the design of the interconnection network topology is not currently automated. They rely heavily on expert knowledge and fail to deliver optimal performance. To this end, we propose an automated design framework for chiplet interconnection network topology, called CINT-AD. To implement CINT-AD, we first investigate topology-related properties from the perspective of design constraints and structural symmetry. Then, using these properties, we develop an automated framework to generate the topology for interposer interconnections between different chiplets. A deadlock-free routing scheme is proposed for the topologies generated by CINT-AD to fully utilize the resources of the interconnection network. Experimental results show that CINT-AD achieves lower average latency and higher throughput compared to existing state-of-the-art topologies. Furthermore, power and area analysis show that the overhead of CINT-AD is negligible.

Hamiltonian cycles of balanced hypercube with disjoint faulty edges

The balanced hypercube BHn, a variant of the hypercube, is a novel interconnection network topology for massive parallel systems. It is showed in [Theor. Comput. Sci. 947 (2023) 113708] that for any edge subset F of BHn there exists a fault-free Hamiltonian cycle in BHn−F for n≥2 with |F|≤5n−7 if the degree of every vertex in BHn−F is at least two and there exist no f4-cycles in BHn−F. In this paper, we consider the existence of Hamiltonian cycles of BHn when F is a matching (a set of disjoint edges), and show that each edge e∉F lies on a fault-free Hamiltonian cycle of BHn−F with n≥2. The number of faulty edges in F can be up to 22n−1, which is exponential to the dimension n.

Ant Mill: an adversarial traffic pattern for low-diameter direct networks

Since today’s HPC and data center systems can comprise hundreds of thousands of servers and beyond, it is crucial to equip them with a network that provides high performance. New topologies proposed to achieve such performance need to be evaluated under different traffic conditions, aiming to closely replicate real-world scenarios. While most optimizations should be guided by common traffic patterns, it is essential to ensure that no pathological traffic pattern can compromise the entire system. Determining synthetic adversarial traffic patterns for a network typically relies on a thorough understanding of its topology and routing. In this paper, we address the problem of identifying a generic adversarial traffic pattern for low-diameter direct interconnection networks. We first focus on Random Regular Graphs (RRGs), which represent a typical case for these networks. Moreover, RRGs have been proposed as topologies for interconnection networks due to their superior scalability and expandability, among other advantages. We introduce Ant Mill, an adversarial traffic pattern for RRGs when using routes of minimal length. Secondly, we demonstrate that the Ant Mill traffic pattern is also adversarial in other low-diameter direct interconnection networks such as Slimfly, Dragonfly, and Projective networks. Ant Mill is thoroughly motivated and evaluated, enabling future studies of low-diameter direct interconnection networks to leverage its findings.

Roman detour domination number of generalized hypercube networks

Generalized hypercube network is an interconnection network topology. The topology of interconnection network usually takes graph as a mathematical model, in which the vertex of graph represents the server and the edge of graph represents the connection between servers. As vertex count increases, the vertex degree of hypercube network increases as well. This has advantages, such as increased performance and reliability. The domination parameters are an important basis for analyzing and measuring the reliability of interconnection networks. In this paper, few properties of generalized hypercube network and Roman detour domination number for minimum dimensional generalized hypercube networks and hypercube networks are discussed. And also we determine the bounds for [Formula: see text] and [Formula: see text].

On Graph Theoretical Properties of Extended Double Star Interconnection Network Topology


 The Extended Double star (EDS) parallel interconnection network with a network controller (NC) is a two-level hybrid structure. It is a large-scale network with the Double star as its basic building block. EDS network has degree (n!+n+1) and diameter ⌊(

Super Structure Fault-Tolerance Assessment of the Generalized Hypercube

Abstract Fault-tolerant performance of a network is the prerequisite and guarantee for the normal operation of a network, which is often characterized by connectivity. Let $H$ denote a connected subgraph of $G$ and $H^{*}$ denote the union of the set of all connected subgraphs of $H$ and the set of the trivial graph. Super $H$-connectivity (resp. super $H^{*}$-connectivity) satisfies the conditions of both super connectivity and $H$-structure connectivity (resp. $H$-substructure connectivity). These two kinds of new connectivity provide a new metric to measure the fault-tolerance of the network, that is, the super structure fault-tolerance. The generalized hypercube $G(m_{r}, m_{r-1},..., m_{1})$ is a universal topology of interconnection networks that contains other commonly used topologies and it has been applied in many data center networks because of its excellent qualities. In this paper, we research the super structure fault-tolerance of $G(m_{r}, m_{r-1},..., m_{1})$ by studying super $H$-connectivity $\kappa ^{\prime}(G|H)$ and super $H^{*}$-connectivity $\kappa ^{\prime}(G|H^{*})$ for $H\in \{K_{1,M},\ C_{3},\ C_{4},\ K_{4}\}$.

Many-to-many edge-disjoint paths in (n,k)-enhanced hypercube under three link-faulty hypotheses

One of the most central issues in interconnection networks of parallel and distributed systems is finding edge-disjoint paths that transmit information. Finding as many as possible many-to-many edge-disjoint paths is conducive to improving the fault-tolerance of such networks. As an interconnection network topology, (n,k)-enhanced hypercube Qn,k (1≤k≤n−1), is a momentous variant of well-known hypercube. For integers 1≤l≤n−1 and n≥2, let δ=0 if 1≤l≤n−k, and δ=1 if n−k+1≤l≤n−1. This paper offers a unified method to determine the minimum cardinalities of faulty links in Qn,k, whose malfunction divides this network into several connected components such that each processor has at least l+δ neighbors, each component contains no less than 2l processors and the number of average neighbors for all processors is at least l+δ, respectively. Under these three different link-faulty assumptions, but for the condition of k=2 and l=n−2, the minimum cardinalities of such faulty links share the same value (n−l−δ+1)2l. And the value in the exceptional case is (n−l−δ)2l+1=2n−1. In other words, we find the maximum numbers of many-to-many edge-disjoint paths of Qn,k under the above three hypotheses, which offers refined measurements for the reliability and fault-tolerance of interconnection networks.

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.

The $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubes

&lt;abstract&gt;&lt;p&gt;At present, the reliability of interconnection networks of multiprocessing systems has become a hot topic of research concern for parallel computer systems. Conditional connectivity is an important parameter to measure the reliability of an interconnected network. In reality, the failure of one node will inevitably have a negative impact on the surrounding nodes. Often it is the specific structures that fail in an interconnected network. Therefore, we propose two novel kinds of connectivity, called $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity, to go for a more accurate measure of the reliability of the network. Hypercube network is the most dominant interconnection network topology used by computer systems today, for example, the famous parallel computing systems Cray $ T3D $, Cray $ T3E $, $ IBM $ Blue Gene, etc. are built with it as the interconnection network topology. In this paper, we obtain the results of the $ g $-extra $ H $-structure connectivity and the $ g $-extra $ H $-substructure connectivity of the hypercubes when the specific structure is $ P_k $ and $ g = 1 $.&lt;/p&gt;&lt;/abstract&gt;

Sufficient Conditions for Oscillations in Competitive Linear-Threshold Brain Networks

Oscillatory activity is highly prevalent in the brain. Oscillations with specific characteristics are associated with a variety of healthy and diseased brain functions. This paper considers two mesoscale brain network models described by linear-threshold and threshold-linear dynamics and takes on the analytical characterization of the emergence of oscillations. The synaptic connectivity is described by an arbitrary network interconnection topology that allows for self-excitatory nodes. We provide a structural characterization for the existence of stable node sets that support asymptotically stable equilibria and identify sufficient conditions for oscillatory behavior in competitive linear-threshold and threshold-linear dynamics. Simulations illustrate our results.

Design and evaluation of an energy efficient DiamondMesh topology for on-chip interconnection networks

Design and evaluation of an energy efficient DiamondMesh topology for on-chip interconnection networks

A Novel Hybrid Hexagonal Star Topology for On-Chip Interconnection Networks

Network-on-Chip (NoC) is an emerging and efficient on-chip interconnection network. NoC is expected to be the communication backbone of next-generation Multi-processor System-on-Chip (MPSoC) architectures. Topology is a crucial design aspect of NoC, as it affects the performance of the interconnection network. This paper proposes a novel, scalable, hybrid Hexagonal Star (HS) topology for on-chip interconnection networks. Properties of the proposed topology have been explored and compared with those of Mesh, Torus and Honeycomb Mesh topologies. The performance of the Hexagonal Star topology has been evaluated and compared with that of Mesh topology for different scenarios. The comparative studies of topological properties have indicated that the proposed topology can be a potential choice for on-chip interconnection networks. The simulation results have shown that the proposed topology outperforms Mesh topology in terms of latency for low traffic loads. For different traffic patterns and traffic loads, HS topology has registered a reduction of packet latency ranging from 15% to 50% and from 9% to 23% for 18 nodes and 32 nodes, respectively, compared to Mesh topology.

Edge-Based Heuristics for Optimizing Shortcut-Augmented Topologies for HPC Interconnects

Interconnection network topology is critical for the overall performance of HPC systems. While many regular and irregular topologies have been proposed in the past, recent work has shown the promise of shortcut-augmented topologies that offer multi-fold reduction in network diameter and hop count over conventional topologies. However, the large number of possible shortcuts creates an enormous design space for this new type of topology, and existing approaches are extremely slow and do not find shortcuts that are globally optimal. In this paper, we propose an efficient heuristic approach, called EdgeCut, which generates high-quality shortcut-augmented topologies. EdgeCut can identify more globally useful shortcuts by making its considerations from the perspective of edges instead of vertices. An additional implementation is proposed that approximates the costly all-pair shortest paths calculation, thereby further speeding up the scheme. Quantitative comparisons over prior work show that the proposed approach achieves a 1982× reduction in search time while generating better or equivalent topologies in 94.9% of the evaluated cases.

Subnetwork Preclusion of (n,k)-Star Networks

The [Formula: see text]-star graph [Formula: see text], which is introduced to address scaling issues of the star graph, is recognized as an attractive interconnection network topology for building multiprocessor systems because of its desirable properties. Let [Formula: see text] be the minimum number of faulty vertices that make every subgraph isomorphic to [Formula: see text] faulty in [Formula: see text] under vertex-failure model, where [Formula: see text]. In this paper, we prove that [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text] and [Formula: see text].

Some Properties of the Balanced Hypercube

As a variant of [Formula: see text], Huang and Wu in [IEEE Transactions on Computers 46 (1997) 484–490] introduced the balanced hypercube [Formula: see text] as an interconnection network topology for computing systems. In this paper, we show that [Formula: see text] is a lexicographic product of two graphs, and using this, we show that every minimum cyclic vertex-cut of [Formula: see text] isolates a 4-cycle, and prove that the edge neighbor connectivity of [Formula: see text] is [Formula: see text].

Subnetwork reliability analysis of bubble-sort graph networks

The bubble-sort graph network Bn is recognized as an attractive interconnection network topology for building multiprocessor computer systems. In this paper, the subnetwork reliability of Bn is analyzed in the presence of node failures. An upper bound and a lower bound on the Bn−1 subnetwork reliability of Bn are established under the probability fault model, and the theoretical results are proved to be in accordance with and near to the simulation results. Moreover, under the node fault model, the mean time to failure to maintain the fault-free status of different number of disjoint Bn−1 subnetworks in Bn is evaluated by using the fixed partitioning and the flexible partitioning, respectively, and it is shown that Bn has better robustness under the flexible partitioning pattern when disjoint Bn−1 subnetworks need to be used.

Unpaired Many-to-Many Disjoint Path Cover of Balanced Hypercubest

A many-to-many [Formula: see text]-disjoint path cover ([Formula: see text]-DPC) of a graph [Formula: see text] is a set of [Formula: see text] vertex-disjoint paths joining [Formula: see text] distinct pairs of source and sink in which each vertex of [Formula: see text] is contained exactly once in a path. The balanced hypercube [Formula: see text], a variant of the hypercube, was introduced as a desired interconnection network topology. Let [Formula: see text] and [Formula: see text] be any two sets of vertices in different partite sets of [Formula: see text] ([Formula: see text]). Cheng et al. in [Appl. Math. Comput. 242 (2014) 127–142] proved that there exists paired many-to-many 2-disjoint path cover of [Formula: see text] when [Formula: see text]. In this paper, we prove that there exists unpaired many-to-many [Formula: see text]-disjoint path cover of [Formula: see text] ([Formula: see text]) from [Formula: see text] to [Formula: see text], which has improved some known results. The upper bound [Formula: see text] is best possible in terms of the number of disjoint paths in unpaired many-to-many [Formula: see text]-DPC of [Formula: see text].

The symmetry property of (n,k)‐arrangement graph

AbstractThe ‐arrangement graph with , is the graph with vertex set the ordered ‐tuples of distinct elements in and with two ‐tuples adjacent if they differ in exactly one of their coordinates. The ‐arrangement graph was proposed by Day and Tripathi in 1992, and is a widely studied interconnection network topology. The Johnson graph with , is the graph with vertex set the ‐element subsets of , and with two ‐element subsets adjacent if their intersection has elements. In 1989, Brouwer, Cohen and Neumaier determined the automorphism group of , and in 2015, Dobson and Malnič proved that a is Cayley graph if and only if , or with being a prime‐power. In this article we prove that , and as a byproduct, is a normal cover of . Furthermore, is a Cayley graph if and only if , , , , , , , , , , , or , where is a prime‐power. Note that the graph is called the ‐star graph, and its automorphism group can be deduced from a general result given by Feng in 2006. In 1998, Chiang and Chen proved that is a Cayley graph on the alternating group , and in 2011, Zhou determined the automorphism group of .

The structure of $k$-Lucas cubes

Fibonacci cubes and Lucas cubes have been studied as alternatives for the classical hypercube topology for interconnection networks. These families of graphs have interesting graph theoretic and enumerative properties. Among the many generalization of Fibonacci cubes are $k$-Fibonacci cubes, which have the same number of vertices as Fibonacci cubes, but the edge sets determined by a parameter $k$. In this work, we consider $k$-Lucas cubes, which are obtained as subgraphs of $k$-Fibonacci cubes in the same way that Lucas cubes are obtained from Fibonacci cubes. We obtain a useful decomposition property of $k$-Lucas cubes which allows for the calculation of basic graph theoretic properties of this class: the number of edges, the average degree of a vertex, the number of hypercubes they contain, the diameter and the radius.

Minimal Feedback Vertex Sets in Honeycomb Networks

A vertex subset of a graph G is called a feedback vertex set if its removal results in an acyclic subgraph. The feedback vertex number (G) is the cardinality of the minimum feedback vertex set of G , which is an important parameter of interconnection network topology. In this paper, we determine the feedback numbers of Honeycomb mesh n HM and Honeycomb torus n HT , i.e. 2 ( ) 9 / 2 15n/2 4 n  HM  n   and 2 ( ) 9 / 2 9 / 2 2 n  HT  n  n  . Comparing these results with those of Zhou, we find that (H) is related to the boundary of Honeycomb network H .