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Parallel and Distributed Systems, IEEE Transactions on

Issue 1 • Date Jan. 2001

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Displaying Results 1 - 7 of 7
  • 2000 reviewers list

    Page(s): 3 - 6
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    Freely Available from IEEE
  • A unified formulation of honeycomb and diamond networks

    Page(s): 74 - 80
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB) |  | HTML iconHTML  

    Honeycomb and diamond networks have been proposed as alternatives to mesh and torus architectures for parallel processing. When wraparound links are included in honeycomb and diamond networks, the resulting structures can be viewed as having been derived via a systematic pruning scheme applied to the links of 2D and 3D tori, respectively. The removal of links, which is performed along a diagonal pruning direction, preserves the network's node-symmetry and diameter, while reducing its implementation complexity and VLSI layout area. In this paper, we prove that honeycomb and diamond networks are special subgraphs of complete 2D and 3D tori, respectively, and show this viewpoint to hold important implications for their physical layouts and routing schemes. Because pruning reduces the node degree without increasing the network diameter, the pruned networks have an advantage when the degree-diameter product is used as a figure of merit. Additionally, if the reduced node degree is used as an opportunity to increase the link bandwidths to equalize the costs of pruned and unpruned networks, a gain in communication performance may result View full abstract»

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  • All-to-all personalized communication in multidimensional torus and mesh networks

    Page(s): 38 - 59
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (16768 KB) |  | HTML iconHTML  

    All-to-all personalized communication commonly occurs in many important parallel algorithms, such as FFT and matrix transpose. This paper presents new algorithms for all-to-all personalized communication or complete exchange in multidimensional torus- or mesh-connected multiprocessors. For an R×C torus or mesh where R⩽C, the proposed algorithms have time complexities of O(C) message startups and O(RC2) message transmissions. The algorithms for three- or higher-dimensional tori or meshes follow a similar structure. Unlike other existing message-combining algorithms in which the number of nodes in each dimension should be a power-of-two and square, the proposed algorithms accommodate non-power-of-two tori or meshes where the number of nodes in each dimension need not be power-of-two and square. In addition, destinations remain fixed over a larger number of steps in the proposed algorithms, thus making them amenable to optimizations. Finally, the data structures used are simple, hence making substantial savings of message-rearrangement time View full abstract»

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  • Parallel solutions of simple indexed recurrence equations

    Page(s): 22 - 37
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    We define a new type of recurrence equations called “Simple Indexed Recurrences” (SIR). In this type of equations, ordinary recurrences are generalized to X[g(i)]=opi(X[f(i)], X[g(i)]), where f, g : {1...n}→{1...m}, opi(x, y) is a binary associative operator and g is distinct, i.e., ∀i≠j g(i)≠g(j). This enables us to model certain sequential loops as a sequence of SIR equations. A parallel algorithm that solves a set of SIR equations will, in fact, parallelize sequential loops of the above type. Such a parallel SIR algorithm must be efficient enough to compete with the O(n) work complexity of the original loop. We show why efficient parallel algorithms for the related problems of list ranking and tree contraction, which require O(n) work, cannot be applied to solving SIR. We instead use repeated iterations of pointer jumping to compute the final values of X[] in n/p·log p steps and n·log p work, with p processors. A sequence of experiments was performed to test the effect of synchronous and asynchronous executions on the actual performance of the algorithm. These experiments show that pointer jumping requires O(n)) work in most practical cases of SIR loops. An efficient solution is given for the special case where we know how to compute the inverse of opi, and finally, useful applications of SIR to the well-known Livermore loops benchmark are presented View full abstract»

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  • Families of optimal fault-tolerant multiple-bus networks

    Page(s): 60 - 73
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (436 KB) |  | HTML iconHTML  

    Optimally fault-tolerant partial-connection multiple-bus networks and their fault-tolerant routing algorithms are presented in this paper. The proposed networks are scalable and provide flexibility in the choice of network parameters determining construction cost, system performance, and fault tolerance, given a fixed number of processors. In this design, when performance begins to fall due to contention, the simple addition of a bus can improve performance without adding costly processors or changing the whole topology, as required for other multiple-bus designs. Also, in situations requiring high reliability, for a fixed number of processors, excellent fault tolerance can be obtained View full abstract»

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  • Symbolic model checking for self-stabilizing algorithms

    Page(s): 81 - 95
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (564 KB) |  | HTML iconHTML  

    A distributed system is said to be self-stabilizing if it converges to safe states regardless of its initial state. In this paper we present our results of using symbolic model checking to verify distributed algorithms against the self-stabilizing property. In general, the most difficult problem with model checking is state explosion; it is especially serious in verifying the self-stabilizing property, since it requires the examination of all possible initial states. So far applying model checking to self-stabilizing algorithms has not been successful due to the problem of state explosion. In order to overcome this difficulty, we propose to use symbolic model checking for this purpose. Symbolic model checking is a verification method which uses Ordered Binary Decision Diagrams (OBDDs) to compactly represent state spaces. Unlike other model checking techniques, this method has the advantage that most of its computations do not depend on the initial states. We show how to verify the correctness of algorithms by means of SMV, a well-known symbolic model checker. By applying the proposed approach to several algorithms in the literature, we demonstrate empirically that the state spaces of self-stabilizing algorithms can be represented by OBDDs very efficiently. Through these case studies, we also demonstrate the usefulness of the proposed approach in detecting errors View full abstract»

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  • On k-set consensus problems in asynchronous systems

    Page(s): 7 - 21
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    In this paper, we investigate the k-set consensus problem in asynchronous distributed systems. In this problem, each participating process begins the protocol with an input value and by the end of the protocol must decide on one value so that at most k total values are decided by all correct processes. We extend previous work by exploring several variations of the problem definition and model, including for the first time investigation of Byzantine failures. We show that the precise definition of the validity requirement, which characterizes what decision values are allowed as a function of the input values and whether failures occur, is crucial to the solvability of the problem. For example, we show that allowing default decisions in case of failures makes the problem solvable for most values of k despite a minority of failures, even in face of the most severe type of failures (Byzantine). We introduce six validity conditions for this problem (all considered in various contexts in the literature), and demarcate the line between possible and impossible for each case. In many cases, this line is different from the one of the originally studied k-set consensus problem View full abstract»

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Aims & Scope

IEEE Transactions on Parallel and Distributed Systems (TPDS) is published monthly. It publishes a range of papers, comments on previously published papers, and survey articles that deal with the parallel and distributed systems research areas of current importance to our readers.

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Meet Our Editors

Editor-in-Chief
David Bader
College of Computing
Georgia Institute of Technology