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Performance Analysis of kary ncube Interconnection Networks
 IEEE Transactions on Computers
, 1988
"... VLSI communication networks are wire limited. The cost of a network is not a function of the number of switches required, but rather a function of the wiring density required to construct the network. This paper analyzes communication networks of varying dimension under the assumption of constant wi ..."
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Cited by 296 (16 self)
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VLSI communication networks are wire limited. The cost of a network is not a function of the number of switches required, but rather a function of the wiring density required to construct the network. This paper analyzes communication networks of varying dimension under the assumption of constant wire bisection. Expressions for the latency, average case throughput, and hotspot throughput of kary n cube networks with constant bisection are derived that agree closely with experimental measurements. It is shown that lowdimensional networks (e.g., tori) have lower latency and higher hotspot throughput than highdimensional networks (e.g., binary ncubes) with the same bisection width. Keywords Communication networks, interconnection networks, concurrent computing, messagepassing multiprocessors, parallel processing, VLSI. 1 Introduction The critical component of a concurrent computer is its communication network. Many algorithms are communication rather than processing limited. Fi...
Algorithms for Parallel Memory I: TwoLevel Memories
, 1992
"... We provide the first optimal algorithms in terms of the number of input/outputs (I/Os) required between internal memory and multiple secondary storage devices for the problems of sorting, FFT, matrix transposition, standard matrix multiplication, and related problems. Our twolevel memory model is n ..."
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Cited by 236 (32 self)
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We provide the first optimal algorithms in terms of the number of input/outputs (I/Os) required between internal memory and multiple secondary storage devices for the problems of sorting, FFT, matrix transposition, standard matrix multiplication, and related problems. Our twolevel memory model is new and gives a realistic treatment of parallel block transfer, in which during a single I/O each of the P secondary storage devices can simultaneously transfer a contiguous block of B records. The model pertains to a largescale uniprocessor system or parallel multiprocessor system with P disks. In addition, the sorting, FFT, permutation network, and standard matrix multiplication algorithms are typically optimal in terms of the amount of internal processing time. The difficulty in developing optimal algorithms is to cope with the partitioning of memory into P separate physical devices. Our algorithms' performance can be significantly better than those obtained by the wellknown but nonopti...
Architecture of FieldProgrammable Gate Arrays: The Effect of Logic Block Functionality on Area Efficiency
 Proceedings of the IEEE
, 1990
"... tures and the programming technologies used to customize them is presented. Programming technologies are compared on the basis of their vola fility, size, parasitic capacitance, resistance, and process technology complexity. FPGA architectures are divided into two constituents: logic block architect ..."
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Cited by 109 (13 self)
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tures and the programming technologies used to customize them is presented. Programming technologies are compared on the basis of their vola fility, size, parasitic capacitance, resistance, and process technology complexity. FPGA architectures are divided into two constituents: logic block architectures and routing architectures. A classijcation of logic blocks based on their granularity is proposed and several logic blocks used in commercially available FPGA ’s are described. A brief review of recent results on the effect of logic block granularity on logic density and pe$ormance of an FPGA is then presented. Several commercial routing architectures are described in the contest of a general routing architecture model. Finally, recent results on the tradeoff between the fleibility of an FPGA routing architecture its routability and density are reviewed. I.
merging, and sorting in parallel models of computation
 in “Proc. 14th Annual ACM Sympos. on Theory of Cornput
, 1982
"... A variety of models have been proposed for the study of synchronous parallel computation. These models are reviewed and some prototype problems are studied further. Two classes of models are recognized, fixed connection networks and models based on a shared memory. Routing and sorting are prototype ..."
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Cited by 105 (3 self)
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A variety of models have been proposed for the study of synchronous parallel computation. These models are reviewed and some prototype problems are studied further. Two classes of models are recognized, fixed connection networks and models based on a shared memory. Routing and sorting are prototype problems for the networks; in particular, they provide the basis for simulating the more powerful shared memory models. It is shown that a simple but important class of deterministic strategies (oblivious routing) is necessarily inefficient with respect to worst case analysis. Routing can be viewed as a special case of sorting, and the existence of an O(log n) sorting algorithm for some n processor fixed connection network has only recently been established by Ajtai, Komlos, and Szemeredi (“15th ACM Sympos. on Theory of Cornput., ” Boston, Mass., 1983, pp. l9). If the more powerful class of shared memory models is considered then it is possible to simply achieve an O(log n loglog n) sort via Valiant’s parallel merging algorithm, which it is shown can be implemented on certain models. Within a spectrum of shared memory models, it is shown that loglogn is asymptotically optimal for n processors to merge two sorted lists containing n elements. 0 1985 Academic Press, Inc.
A Complexity Theory for VLSI
 TECHNICAL REPORT
, 1980
"... The established methodologies for studying computational complexity can be applied to the new problems posed by very largescale integrated (VLSI) circuits. This thesis develops a “VLSI model of computation” and derives upper and lower bounds on the silicon area and time required to solve the proble ..."
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Cited by 105 (1 self)
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The established methodologies for studying computational complexity can be applied to the new problems posed by very largescale integrated (VLSI) circuits. This thesis develops a “VLSI model of computation” and derives upper and lower bounds on the silicon area and time required to solve the problems of sorting and discrete Fourier transformation. In particular, the area A and time T taken by any VLSI chip using any algorithm to perform an $N$point Fourier transform must satisfy $AT^2 \geq c N^2 \log^2 N$, for some fixed $c > 0$. A more general result for both sorting and Fourier transformation is that $AT^{2x} = \Omega(N^{1+x} \log^{2x} N)$ for any $x$ in the range $0 < x < 1$. Also, the energy dissipated by a VLSI chip during the solution of either of these problems is at least $\Omega(N^{3/2} \log N)$. The tightness of these bounds is demonstrated by the existence of nearly optimal circuits for both sorting and Fourier transformation. The circuits based on the shuffleexchange interconnection pattern are fast but large: $T = O(\log^2 N)$ for Fourier transformation, $T = O(\log^3 N)$ for sorting; both have area $A$ of at most $O(N^2 / \log{1/2} N)$. The circuits based on the mesh interconnection pattern are slow but small: $T = O(N^{1/2} \log\log N)$, $A = O(N \log^2 N)$.
Basic Techniques for the Efficient Coordination of Very Large Numbers of Cooperating Sequential Processors
, 1981
"... In this paper we implement several basic operating system primitives by using a "replaceadd" operation, which can supersede the standard "test and set", and which appears to be a universal primitive for efficiently coordinating large numbers of independently acting sequential processors. We also pr ..."
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Cited by 89 (2 self)
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In this paper we implement several basic operating system primitives by using a "replaceadd" operation, which can supersede the standard "test and set", and which appears to be a universal primitive for efficiently coordinating large numbers of independently acting sequential processors. We also present a hardware implementation of replaceadd that permits multiple replaceadds to be processed nearly as efficiently as loads and stores. Moreover, the crucial special case of concurrent replaceadds updating the same variable is handled particularly well: If every PE simultaneously addresses a replaceadd at the same variable, all these requests are satisfied in the time required to process just one request.
A methodology for designing, modifying, and implementing Fourier transform algorithms on various architectures
 IEEE Trans. on Circuits and Systems
, 1990
"... ..."
Special Purpose Parallel Computing
 Lectures on Parallel Computation
, 1993
"... A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing ..."
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Cited by 77 (5 self)
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A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing [365] demonstrated that, in principle, a single general purpose sequential machine could be designed which would be capable of efficiently performing any computation which could be performed by a special purpose sequential machine. The importance of this universality result for subsequent practical developments in computing cannot be overstated. It showed that, for a given computational problem, the additional efficiency advantages which could be gained by designing a special purpose sequential machine for that problem would not be great. Around 1944, von Neumann produced a proposal [66, 389] for a general purpose storedprogram sequential computer which captured the fundamental principles of...
Deterministic Sorting in Nearly Logarithmic Time on the Hypercube and Related Computers
 Journal of Computer and System Sciences
, 1996
"... This paper presents a deterministic sorting algorithm, called Sharesort, that sorts n records on an nprocessor hypercube, shuffleexchange, or cubeconnected cycles in O(log n (log log n) 2 ) time in the worst case. The algorithm requires only a constant amount of storage at each processor. Th ..."
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Cited by 67 (10 self)
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This paper presents a deterministic sorting algorithm, called Sharesort, that sorts n records on an nprocessor hypercube, shuffleexchange, or cubeconnected cycles in O(log n (log log n) 2 ) time in the worst case. The algorithm requires only a constant amount of storage at each processor. The fastest previous deterministic algorithm for this problem was Batcher's bitonic sort, which runs in O(log 2 n) time. Supported by an NSERC postdoctoral fellowship, and DARPA contracts N0001487K825 and N00014 89J1988. 1 Introduction Given n records distributed uniformly over the n processors of some fixed interconnection network, the sorting problem is to route the record with the ith largest associated key to processor i, 0 i ! n. One of the earliest parallel sorting algorithms is Batcher's bitonic sort [3], which runs in O(log 2 n) time on the hypercube [10], shuffleexchange [17], and cubeconnected cycles [14]. More recently, Leighton [9] exhibited a boundeddegree,...
MULTIPROCESSOR SCHEDULING TO ACCOUNT FOR INTERPROCESSOR COMMUNICATION
, 1991
"... Interprocessor communication (PC) overheads have emerged as the major performance limitation in parallel processing systems, due to the transmission delays, synchronization overheads, and conflicts for shared communication resources created by data exchange. Accounting for these overheads is essenti ..."
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Cited by 67 (11 self)
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Interprocessor communication (PC) overheads have emerged as the major performance limitation in parallel processing systems, due to the transmission delays, synchronization overheads, and conflicts for shared communication resources created by data exchange. Accounting for these overheads is essential for attaining efficient hardware utilization. This thesis introduces two new compiletime heuristics for scheduling precedence graphs onto multiprocessor architectures, which account for interprocessor communication overheads and interconnection constraints in the architecture. These algorithms perform scheduling and routing simultaneously to account for irregular interprocessor interconnections, and schedule all communications as well as all computations to eliminate shared resource contention. The first technique, called dynamiclevel scheduling, modifies the classical HLFET list scheduling strategy to account for IPC and synchronization overheads. By using dynamically changing priorities to match nodes and processors at each step, this technique attains an equitable tradeoff between load balancing and interprocessor communication cost. This method is fast, flexible, widely targetable, and displays promising perforrnance. The second technique, called declustering, establishes a parallelism hierarchy upon the precedence graph using graphanalysis techniques which explicitly address the tradeoff between exploiting parallelism and incurring communication cost. By systematically decomposing this hierarchy, the declustering process exposes parallelism instances in order of importance, assuring efficient use of the available processing resources. In contrast with traditional clustering schemes, this technique can adjust the level of cluster granularity to suit the characteristics of the specified architecture, leading to a more effective solution.