Fault-tolerant meshes and hypercubes with minimal numbers of spares

Many parallel computers consist of processors connected in the form of a d-dimensional mesh or hypercube. Two- and three-dimensional meshes have been shown to be efficient in manipulating images and dense matrices, whereas hypercubes have been shown to be well suited to divide-and-conquer algorithms requiring global communication. However, even a single faulty processor or communication link can seriously affect the performance of these machines. This paper presents several techniques for tolerating faults in d-dimensional mesh and hypercube architectures. Our approach consists of adding spare processors and communication links so that the resulting architecture will contain a fault-free mesh or hypercube in the presence of faults. We optimize the cost of the fault-tolerant architecture by adding exactly k spare processors (while tolerating up to k processor and/or link faults) and minimizing the maximum number of links per processor. For example, when the desired architecture is a d-dimensional mesh and k = 1, we present a fault-tolerant architecture that has the same maximum degree as the desired architecture (namely, 2d) and has only one spare processor. We also present efficient layouts for fault-tolerant two- and three-dimensional meshes, and show how multiplexers and buses can be used to reduce the degree of fault-tolerant architectures. Finally, we give constructions for fault-tolerant tori, eight-connected meshes, and hexagonal meshes

A novel QoS multicast model in mobile ad hoc networks

2004-2005 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe

Recursive Cube of Rings: A new topology for interconnection networks

In this paper, we introduce a family of scalable interconnection network topologies, named Recursive Cube of Rings (RCR), which are recursively constructed by adding ring edges to a cube. RCRs possess many desirable topological properties in building scalable parallel machines, such as fixed degree, small diameter, wide bisection width, symmetry, fault tolerance, etc. We first examine the topological properties of RCRs. We then present and analyze a general deadlock-free routing algorithm for RCRs. Using a complete binary tree embedded into an RCR with expansion-cost approximating to one, an efficient broadcast routing algorithm on RCRs is proposed. The upper bound of the number of message passing steps in one broadcast operation on a general RCR is also derived.published_or_final_versio

Interconnection networks for parallel and distributed computing

Parallel computers are generally either shared-memory machines or distributed- memory machines. There are currently technological limitations on shared-memory architectures and so parallel computers utilizing a large number of processors tend tube distributed-memory machines. We are concerned solely with distributed-memory multiprocessors. In such machines, the dominant factor inhibiting faster global computations is inter-processor communication. Communication is dependent upon the topology of the interconnection network, the routing mechanism, the flow control policy, and the method of switching. We are concerned with issues relating to the topology of the interconnection network. The choice of how we connect processors in a distributed-memory multiprocessor is a fundamental design decision. There are numerous, often conflicting, considerations to bear in mind. However, there does not exist an interconnection network that is optimal on all counts and trade-offs have to be made. A multitude of interconnection networks have been proposed with each of these networks having some good (topological) properties and some not so good. Existing noteworthy networks include trees, fat-trees, meshes, cube-connected cycles, butterflies, Möbius cubes, hypercubes, augmented cubes, k-ary n-cubes, twisted cubes, n-star graphs, (n, k)-star graphs, alternating group graphs, de Bruijn networks, and bubble-sort graphs, to name but a few. We will mainly focus on k-ary n-cubes and (n, k)-star graphs in this thesis. Meanwhile, we propose a new interconnection network called augmented k-ary n- cubes. The following results are given in the thesis.1. Let k ≥ 4 be even and let n ≥ 2. Consider a faulty k-ary n-cube Q(^k_n) in which the number of node faults f(_n) and the number of link faults f(_e) are such that f(_n) + f(_e) ≤ 2n - 2. We prove that given any two healthy nodes s and e of Q(^k_n), there is a path from s to e of length at least k(^n) - 2f(_n) - 1 (resp. k(^n) - 2f(_n) - 2) if the nodes s and e have different (resp. the same) parities (the parity of a node Q(^k_n) in is the sum modulo 2 of the elements in the n-tuple over 0, 1, ∙∙∙ , k - 1 representing the node). Our result is optimal in the sense that there are pairs of nodes and fault configurations for which these bounds cannot be improved, and it answers questions recently posed by Yang, Tan and Hsu, and by Fu. Furthermore, we extend known results, obtained by Kim and Park, for the case when n = 2.2. We give precise solutions to problems posed by Wang, An, Pan, Wang and Qu and by Hsieh, Lin and Huang. In particular, we show that Q(^k_n) is bi-panconnected and edge-bipancyclic, when k ≥ 3 and n ≥ 2, and we also show that when k is odd, Q(^k_n) is m-panconnected, for m = (^n(k - 1) + 2k - 6’ / ‘_2), and (k -1) pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Q(^k_n) even in the presence of a faulty processor.3. We define an interconnection network AQ(^k_n) which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube Q(^k_n) has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube Q(^k_n) - is a Cayley graph (and so is vertex-symmetric); has connectivity 4n - 2, and is such that we can build a set of 4n - 2 mutually disjoint paths joining any two distinct vertices so that the path of maximal length has length at most max{{n- l)k- (n-2), k + 7}; has diameter [(^k) / (_3)] + [(^k - 1) /( _3)], when n = 2; and has diameter at most (^k) / (_4) (n+ 1), for n ≥ 3 and k even, and at most [(^k)/ (_4) (n + 1) + (^n) / (_4), for n ^, for n ≥ 3 and k odd.4. We present an algorithm which given a source node and a set of n - 1 target nodes in the (n, k)-star graph S(_n,k) where all nodes are distinct, builds a collection of n - 1 node-disjoint paths, one from each target node to the source. The collection of paths output from the algorithm is such that each path has length at most 6k - 7, and the algorithm has time complexity O(k(^3)n(^4))

CLEX: Yet Another Supercomputer Architecture?

We propose the CLEX supercomputer topology and routing scheme. We prove that CLEX can utilize a constant fraction of the total bandwidth for point-to-point communication, at delays proportional to the sum of the number of intermediate hops and the maximum physical distance between any two nodes. Moreover, % applying an asymmetric bandwidth assignment to the links, all-to-all communication can be realized $(1+o(1))$-optimally both with regard to bandwidth and delays. This is achieved at node degrees of $n^{\varepsilon}$, for an arbitrary small constant $\varepsilon\in (0,1]$. In contrast, these results are impossible in any network featuring constant or polylogarithmic node degrees. Through simulation, we assess the benefits of an implementation of the proposed communication strategy. Our results indicate that, for a million processors, CLEX can increase bandwidth utilization and reduce average routing path length by at least factors $10$ respectively $5$ in comparison to a torus network. Furthermore, the CLEX communication scheme features several other properties, such as deadlock-freedom, inherent fault-tolerance, and canonical partition into smaller subsystems

Properties and Algorithms of the KCube Interconnection Networks

The KCube interconnection network was first introduced in 2010 in order to exploit the good characteristics of two well-known interconnection networks, the hypercube and the Kautz graph. KCube links up multiple processors in a communication network with high density for a fixed degree. Since the KCube network is newly proposed, much study is required to demonstrate its potential properties and algorithms that can be designed to solve parallel computation problems. In this thesis we introduce a new methodology to construct the KCube graph. Also, with regard to this new approach, we will prove its Hamiltonicity in the general KC(m; k). Moreover, we will find its connectivity followed by an optimal broadcasting scheme in which a source node containing a message is to communicate it with all other processors. In addition to KCube networks, we have studied a version of the routing problem in the traditional hypercube, investigating this problem: whether there exists a shortest path in a Qn between two nodes 0n and 1n, when the network is experiencing failed components. We first conditionally discuss this problem when there is a constraint on the number of faulty nodes, and subsequently introduce an algorithm to tackle the problem without restrictions on the number of nodes

Measuring and Understanding Throughput of Network Topologies

High throughput is of particular interest in data center and HPC networks. Although myriad network topologies have been proposed, a broad head-to-head comparison across topologies and across traffic patterns is absent, and the right way to compare worst-case throughput performance is a subtle problem. In this paper, we develop a framework to benchmark the throughput of network topologies, using a two-pronged approach. First, we study performance on a variety of synthetic and experimentally-measured traffic matrices (TMs). Second, we show how to measure worst-case throughput by generating a near-worst-case TM for any given topology. We apply the framework to study the performance of these TMs in a wide range of network topologies, revealing insights into the performance of topologies with scaling, robustness of performance across TMs, and the effect of scattered workload placement. Our evaluation code is freely available

Simulation of Meshes in a Faulty Supercube with Unbounded Expansion

[[abstract]]Reconfiguring meshes in a faulty Supercube is investigated in the paper. The result can readily be used in the optimal embedding of a mesh (or a torus) of processors in a faulty Supercube with unbounded expansion. There are embedding algorithms proposed in this paper. These embedding algorithms show a mesh with any number of nodes can be embedded into a faulty Supercube with load 1, congestion 1, and dilation 3 such that O(n2-w2) faults can be tolerated, where n is the dimension of the Supercube and 2w is the number of nodes of the mesh. The meshes and hypercubes are widely used interconnection architectures in parallel computing, grid computing, sensor network, and cloud computing. In addition, the Supercubes are superior to hypercube in terms of embedding a mesh and torus under faults. Therefore, we can easily port the parallel or distributed algorithms developed for these structuring of mesh and torus to the Supercube.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]KO