Large-scale Multiprocessor Systems Research Articles

The g-Good-Neighbor Conditional Diagnosability of Exchanged Crossed Cube under the MM* Model

Diagnosability plays an important role in appraising the reliability and fault tolerance of symmetrical multiprocessor systems. The novel g-good-neighbor conditional diagnosability restrains that every fault-free node contains at least g fault-free neighbors and is suitable for large scale multiprocessor systems, attracting a lot of research attention. The relationships between the g-good-neighbor connectivity and g-good-neighbor diagnosability of graphs under the MM* model are separately studied, but only applicable in regular graphs or just ranges rather than exact values. As a promising network structure, in 2019, Guo et al. obtained that the g-good-neighbor diagnosability of the exchanged crossed cube (ECQ(s,t)) under the PMC model is 2g(s+2−g)−1 (t≥s>g). We noticed that the exact value of the g-good-neighbor diagnosability of ECQ(s,t) under the MM* model is still to be determined. In this paper, by proving the upper and lower bounds of the g-good-neighbor diagnosability of ECQ(s,t), for the first time, we derive that the exact value of its g-good-neighbor diagnosability under the MM* model is tgm(ECQ(s,t))=2g(s+2−g)−1 (t≥s>g), achieving the unity of the g-good-neighbor diagnosability of ECQ(s, t) under both the PMC model and MM* model. Towards the end, simulation experiments are conducted to evaluate the correctness and effectiveness of our conclusion. Our research provides an important supplement to the g-good-neighbor diagnosability of ECQ(s,t).

Distance Optimally Edge Connectedness of Arrangement Graph Based on Subgraph Fault Pattern

Large-scale multiprocessor systems or multicomputer systems based on networking have been extensively used in the big data era and social network. Fault tolerance is becoming an essential attribute in multiprocessor systems with the increase of the system scale. For any distinct vertices [Formula: see text], the local connectivity of [Formula: see text] and [Formula: see text], denoted by [Formula: see text], is the maximum number of independent [Formula: see text]-paths in system graph [Formula: see text]. The local edge connectivity of [Formula: see text], [Formula: see text], [Formula: see text], is defined similarly. For any [Formula: see text], [Formula: see text], if [Formula: see text] (or [Formula: see text], then [Formula: see text] is [Formula: see text]-distance optimally (edge) connected, where [Formula: see text] is the diameter of [Formula: see text] and [Formula: see text] is the degree of [Formula: see text]. For any integers [Formula: see text] subject to [Formula: see text], if [Formula: see text] is [Formula: see text]-distance optimally (edge) connected, then we call [Formula: see text] is [Formula: see text]-distance local optimally (edge) connected. In this work, we show that [Formula: see text] ([Formula: see text] is [Formula: see text]-arrangement graph) is [Formula: see text]-distance local optimally edge connected for [Formula: see text] and [Formula: see text].

Reliability of Divide-and-Swap Cube Based on r-Component Connectivity and Diagnosability

When performing big data processing and high-performance computing, large-scale multiprocessor systems have always been committed to ensuring high reliability and fault tolerance. Connectivity and diagnosability are two important metrics to evaluate the fault tolerance and reliability of interconnection networks. In this paper, we determine [Formula: see text]-component connectivity and diagnosability of divide-and-swap cube [Formula: see text]. In detail, we show that, for [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] under the PMC and MM[Formula: see text] models.

Reliability assessment for modified bubble-sort networks

In large-scale multiprocessor systems, it is significant to estimate the reliability of the interconnection networks. The κk and λk are two generalized measurements of reliability for networks. The κk (λk) of G is the minimum cardinality of a set of vertices (edges) of G, if any, whose deletion disconnects G, and every remaining component has minimum degree at least k. For the modified bubble-sort networks MBn, this paper proves κk(MBn)=λk(MBn)=2k(n−k) for k≤n/2. The conclusions extend some known results in the literature, imply that to make a modified bubble-sort network MBn disconnected with all remaining vertices have at least k neighbors, at least 2k(n−k) vertices or edges have to be faulty.

Subgraph-based Strong Menger Connectivity of Hypercube and Exchanged Hypercube

Large scale multiprocessor systems or multicomputer systems, taking interconnection networks as underlying topologies, have been widely used in the big data era. Fault tolerance is becoming an essential attribute in multiprocessor systems as the number of processors is getting larger. A connected graph [Formula: see text] is called strong Menger (edge) connected if, for any two distinct vertices [Formula: see text] and [Formula: see text], there are [Formula: see text] vertex (edge)-disjoint paths between them. Exchanged hypercube [Formula: see text], as a variant of hypercube [Formula: see text], remains lots of preferable fault tolerant properties of hypercube. In this paper, we show that [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] are strong Menger (edge) connected, respectively. Moreover, as a by-product, for dual cube [Formula: see text], one popular generalization of hypercube, [Formula: see text] is also showed to be strong Menger (edge) connected, where [Formula: see text].

The h-restricted connectivity of the generalized hypercubes

Connectivity is an important index in evaluating the reliability and fault tolerant ability of interconnection network. However the traditional connectivity is inappropriate for large scale multiprocessor systems. The h-restricted connectivity, as a generalization of traditional connectivity, was proposed to estimate the reliability of interconnection networks more accurately. For an interconnection network G and a positive integer h, the cardinality of a vertex subset F is called the h-restricted connectivity of G, denoted κh(G), if F is the minimum vertex set subject to that G−F is disconnected and δ(G−F)≥h. In this paper, we investigate the h-restricted connectivity of the generalized hypercube G(mr,mr−1,…,m1). Specially, we determine that κh(G(mr,mr−1,…,m1))=(h+1)κ(G(mr,mr−1,…,m1))−mmaxh for 1≤h≤min⁡{⌊mr2⌋−1,mmin−1,r}, where κ(G(mr,mr−1,…,m1)) is the connectivity of the generalized hypercube, mmax=max⁡{mr,mr−1,…,m1} and mmin=min⁡{mr,mr−1,…,m1}.

Relationship between extra edge connectivity and component edge connectivity for regular graphs

A conditional connectivity is the generalization of the traditional connectivity and can provide more accurate measures regarding the reliability of a large-scale multiprocessor system. The extra edge connectivity and component edge connectivity are two parameters for the reliability evaluation. Although these two measures have attracted considerable attention and been determined for many classes of graphs in recent years, they are established independently. In this paper, we determine the relationship between extra edge connectivities and component edge connectivities of regular networks. Using this relationship, the extra edge connectivity and component edge connectivity are explored for some well-known graphs, including BC graphs, data center networks, augmented k-ary n-cubes, hierarchical star networks, burnt pancake graphs, (n,k)-star graphs, etc.

Characterizations of Minimum Structure- and Substructure-Cuts of Hypercubes

Abstract For a graph G and a connected subgraph H of G, denote by ℋ(G;H) the set of subgraphs of G which are isomorphic to H and denote by ℋS(G;H) the union of sets of subgraphs of T, where T ranges over all the elements in ℋ(G;H). An H-structure-cut (respectively, H-substructure-cut) of G is a subset of ℋ(G;H) (respectively, ℋS(G;H)), if any, whose removal disconnects G. The H-structure connectivity (respectively, H-substructure connectivity) is the cardinality of a minimum H-structure-cut (respectively, H-substructure-cut) of G. The hypercube is one of the most attractive interconnection networks for large-scale multiprocessor computer systems. In this paper, we will characterize the minimum H-structure-cuts and the minimum H-substructure-cuts of hypercubes for H∈{K1,1,K1,2,K1,3,C4}.

Embedding fault-free hamiltonian paths with prescribed linear forests into faulty ternary n-cubes

The k-ary n-cube is an important underlying topology for large-scale multiprocessor systems. A linear forest in a graph is a subgraph each component of which is a path. In this paper, we investigate the problem of embedding hamiltonian paths passing through a prescribed linear forest in ternary n-cubes with faulty edges. Given a faulty edge set F with at most 2n−3 edges and a linear forest L with at most 2n−3−|F| edges, for two distinct vertices in the ternary n-cube, we show that the ternary n-cube admits a fault-free hamiltonian path between u and v passing through L if and only if none of the paths in L has u or v as internal vertices or both of them as end-vertices.

Embedding various cycles with prescribed paths into [formula omitted]-ary [formula omitted]-cubes

The k-ary n-cube has been one of the most popular interconnection networks for large-scale multi-processor systems and data centers. In this study, we investigate the problem of embedding cycles of various lengths passing through prescribed paths in the k-ary n-cube. For n≥2 and k≥5 with k odd, we prove that every path with length h (1≤h≤2n−1) in the k-ary n-cube lies on cycles of every length from h+(k−1)(n−1)/2+k to kn inclusive.

The g-good-neighbor diagnosability of (n,k)-star graphs

Many large-scale multiprocessor or multi-computer systems take interconnection networks as underlying topologies. Fault diagnosis is especially important to identify fault tolerability of such systems. The g-good-neighbor (conditional) diagnosability such that every fault-free node has at least g fault-free neighbors is a novel measure of diagnosability. In this paper, we show that the g-good-neighbor diagnosability of the (n,k)-star graph Sn,k under the PMC model (2≤k≤n−1 and 1≤g≤n−k) and the comparison model (2≤k≤n−1 and 2≤g≤n−k) is n+g(k−1)−1, respectively. In addition, we derive that 1-good-neighbor diagnosability of Sn,k under the comparison model is n+k−2 for 3≤k≤n−1 and n≥4. As a supplement, we also derive that the g-good-neighbor diagnosability of the (n,1)-star graph Sn,1 (1≤g≤⌊n/2⌋−1 and n≥4) under the PMC model and the comparison model is ⌈n/2⌉−1, respectively.

Various cycles embedding in faulty balanced hypercubes

Quite a lot of interconnection networks are served as the underlying topologies of large-scale multiprocessor systems. The hypercube is one of the most popular interconnection networks. In this paper we consider the balanced hypercube, which is a variant of the hypercube. Huang and Wu showed that the balanced hypercube has better properties than hypercube with the same number of links and processors. Let Fe be the set of faulty edges in an n-dimensional balanced hypercube BHn, where n⩾2. In this paper, we consider BHn with |Fe|⩽2n-3 faulty edges and prove that every fault-free edge lies on a fault-free cycle of every even length from 6 to 22n in BHn-Fe. Furthermore, we prove that the lower limit of the length 6 is sharp by giving a counter example.

Conditional connectivity of recursive interconnection networks respect to embedding restriction

Large-scale multiprocessor systems always take some recursive interconnection networks as underlying topologies. Let Gn be an n-dimensional recursive interconnection network. The m-embedding-restricted connectivity ζm(Gn) (resp. the m-embedding-restricted edge connectivity ηm(Gn)) of Gn is the cardinality of a minimum subset of nodes (resp. edges), if any, whose deletion disconnects Gn and each node of the remaining components lies in an undamaged m-dimensional sub-network Gm. In this paper, we present some relationships between the proposed indices and other conditional connectivity indices in general recursive interconnection networks. We give some bounds on these two indices in k-ary n-cubes and bubble-sort networks. In addition, we determine these two indices in k-ary n-cubes and bubble-sort networks in some cases.

Design of 4-disjoint gamma interconnection network layouts and reliability analysis of gamma interconnection Networks

Multistage interconnection networks (MINs) are widely used for reliable data communication in a tightly coupled large-scale multiprocessor system. High reliability of MINs can be achieved using fault tolerance techniques. The fault tolerance is generally achieved by disjoint paths available through multiple connectivity options. The gamma interconnection network (GIN) is a class of fault tolerant MINs providing alternate paths for source---destination node pairs. Various 2-disjoint and 3-disjoint GIN architectures have been presented in the literature. In this paper, two new designs of 4-disjoint paths multistage interconnection networks, called 4-disjoint gamma interconnection networks (4DGIN-1 and 4DGIN-2) are proposed. The proposed 4DGINs provide four disjoint paths for each source---destination pair and can tolerate three switches/link failures in intermediate interconnection layers. Proposed designs are highly reliable GIN with higher fault-tolerant capability than other gamma networks at low cost. Terminal pair reliabilities of proposed designs and various other 2-disjoint and 3-disjoint GINs are evaluated, analyzed and compared. Reliability values of proposed designs are found higher.

AWGR-Based Optical Topologies for Scalable and Efficient Global Communications in Large-Scale Multi-Processor Systems

In large-scale multi-processor computing systems, global communications are typically supported by an auxiliary network (e.g., IBM Blue Gene) or with hardware support in the network (e.g., NEC Earth Simulator). We explore the potential for realizing efficient global communications that can scale beyond a million processors by harnessing the unique parallelism and wavelength routing properties of optical devices. Specifically, we use an arrayed waveguide grating router (AWGR) device as the basic building block in realizing scalable global communication. The AWGR is a passive switch fabric (wavelength router) that uses multiple wavelengths to interconnect outputs and inputs by following a specific cyclic wavelength routing (permutation) pattern. We analyze different network topologies using AWGR devices for barrier synchronization and propose techniques to pick parameters of the network for a given number of processors. We compare the performance and energy consumption for barrier synchronization with what is achievable with state-of-the-art electrical networks.

Conditional connectivity of star graph networks under embedding restriction

The n-dimensional star graph Sn is one of the most attractive interconnection networks of large scale multiprocessor systems. The k-embedding-restricted (edge) connectivity (ηk(Sn)) ζk(Sn) of Sn is defined to be the cardinality of a minimum subset of (edges) nodes, if any, whose deletion disconnects Sn and each node of the remaining components lies in an undamaged k-dimensional substar Sk. In this paper, we investigate the k-embedding-restricted (edge) connectivity of Sn and determine the values of ηk(Sn) and ζk(Sn) for some k’s.

Accelerating UNISIM-Based Cycle-Level Microarchitectural Simulations on Multicore Platforms

UNISIM has been shown to ease the development of simulators for multi-/many-core systems. However, UNISIM cycle-level simulations of large-scale multiprocessor systems could be very time consuming. In this article, we propose a systematic framework for accelerating UNISIM cycle-level simulations on multicore platforms. The proposed framework relies on exploiting the fine-grained parallelism within the simulated cycles using POSIX threads. A multithreaded simulation engine has been devised from the single-threaded UNISIM SystemC engine to facilitate the exploitation of inherent parallelism. An adaptive technique that manages the overall computation workload by adjusting the number of threads employed at any given time is proposed. In addition, we have introduced a technique to balance the workloads of multithreaded executions. This load balancing involves the distributions of SystemC objects among threads. A graph-partitioning-based technique has been introduced to automate such distributions. Finally, two strategies are proposed for realizing nonautomated and fully automated adaptive multithreaded simulations, respectively. Our investigations show that notable acceleration can be achieved by deploying the proposed framework. In particular, we show that simulations on an 8-core multicore platform can provide for close to 6X speedups when simulating many-core systems with large number of cores.

On MPSoC Software Execution at the Transaction Level

This article presents a wide variety of techniques for realizing transaction-level models of the increasingly large-scale multiprocessor systems on chip. It describes how such models of hardware allow subsequent software integration and system performance evaluation.

FAULT DIAGNOSIS OF MULTIPROCESSOR SYSTEMS BASED ON GENETIC AND ESTIMATION OF DISTRIBUTION ALGORITHMS: A PERFORMANCE EVALUATION

As faults are unavoidable in large scale multiprocessor systems, it is important to be able to determine which units of the system are working and which are faulty. System-level diagnosis is a long-standing realistic approach to detect faults in multiprocessor systems. Diagnosis is based on the results of tests executed on the system units. In this work we evaluate the performance of evolutionary algorithms applied to the diagnosis problem. Experimental results are presented for both the traditional genetic algorithm (GA) and specialized versions of the GA. We then propose and evaluate specialized versions of Estimation of Distribution Algorithms (EDA) for system-level diagnosis: the compact GA and Population-Based Incremental Learning both with and without negative examples. The evaluation was performed using four metrics: the average number of generations needed to find the solution, the average fitness after up to 500 generations, the percentage of tests that got to the optimal solution and the average time until the solution was found. An analysis of experimental results shows that more sophisticated algorithms converge faster to the optimal solution.

A new presentation of Metacubes for algorithmic design and case studies: Parallel prefix computation and parallel sorting

A versatile family of interconnection networks alternative to hypercubes, called Metacubes, has been proposed for building extremely large scale multiprocessor systems with a small number of links per node. A Metacube MC(k, m) connects 22 km + k nodes with only k + m links per node. Metacube can be used to build parallel computing systems of very large scale with a small number of links per node. In this paper, we propose a new presentation of Metacube for algorithmic design. Based on the new presentation, we give efficient algorithms for parallel prefix computation and parallel sorting on Metacubes, respectively. The algorithm for prefix computation runs in 2 km (k + 1) + k communication steps and 2 k + 1 m + 2k computation steps on MC(k, m). The sort algorithm runs in O(2 km + k)2 computation steps and O(2 km (2k + 1) + k)2 communication steps on MC(k, m).