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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 297 (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...
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 189 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Limits on Interconnection Network Performance
 IEEE Transactions on Parallel and Distributed Systems
, 1991
"... As the performance of interconnection networks becomes increasingly limited by physical constraints in highspeed multiprocessor systems, the parameters of highperformance network design must be reevaluated, starting with a close examination of assumptions and requirements. This paper models networ ..."
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Cited by 177 (4 self)
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As the performance of interconnection networks becomes increasingly limited by physical constraints in highspeed multiprocessor systems, the parameters of highperformance network design must be reevaluated, starting with a close examination of assumptions and requirements. This paper models network latency, taking both switch and wire delays into account. A simple closed form expression for contention in buffered, direct networks is derived and is found to agree closely with simulations. The model includes the effects of packet size and communication locality. Network analysis under various constraints (such as fixed bisection width, fixed channel width, and fixed node size) and under different workload parameters (such as packet size, degree of communication locality, and network request rate) reveals that performance is highly sensitive to these constraints and workloads. A twodimensional network has the lowest latency only when switch delays and network contention are ignored, but...
A Framework For Solving Vlsi Graph Layout Problems
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1984
"... This paper introduces a new divideandconquer framework for VLSI graph layout. Universally close upper and lower bounds are obtained for important cost functions such as layout area and propagation delay. The framework is also effectively used to design regular and configurable layouts, to assemble ..."
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Cited by 133 (4 self)
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This paper introduces a new divideandconquer framework for VLSI graph layout. Universally close upper and lower bounds are obtained for important cost functions such as layout area and propagation delay. The framework is also effectively used to design regular and configurable layouts, to assemble large networks of processors using restructurable chips, and to configure networks around faulty processors. It is also shown how good graph partitioning heuristics may be used to develop a provably good layout strategy.
Randomized routing and sorting on fixedconnection networks
 Journal of Algorithms
, 1994
"... This paper presents a general paradigm for the design of packet routing algorithms for fixedconnection networks. Its basis is a randomized online algorithm for scheduling any set of N packets whose paths have congestion c on any boundeddegree leveled network with depth L in O(c + L + log N) steps ..."
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Cited by 88 (13 self)
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This paper presents a general paradigm for the design of packet routing algorithms for fixedconnection networks. Its basis is a randomized online algorithm for scheduling any set of N packets whose paths have congestion c on any boundeddegree leveled network with depth L in O(c + L + log N) steps, using constantsize queues. In this paradigm, the design of a routing algorithm is broken into three parts: (1) showing that the underlying network can emulate a leveled network, (2) designing a path selection strategy for the leveled network, and (3) applying the scheduling algorithm. This strategy yields randomized algorithms for routing and sorting in time proportional to the diameter for meshes, butterflies, shuffleexchange graphs, multidimensional arrays, and hypercubes. It also leads to the construction of an areauniversal network: an Nnode network with area Θ(N) that can simulate any other network of area O(N) with slowdown O(log N).
The Power of Reconfiguration
, 1998
"... This paper concerns the computational aspects of the reconfigurable network model. The computational power of the model is investigated under several network topologies and assuming several variants of the model. In particular, it is shown that there are reconfigurable machines based on simple netwo ..."
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Cited by 85 (7 self)
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This paper concerns the computational aspects of the reconfigurable network model. The computational power of the model is investigated under several network topologies and assuming several variants of the model. In particular, it is shown that there are reconfigurable machines based on simple network topologies, that are capable of solving large classes of problems in constant time. These classes depend on the kinds of switches assumed for the network nodes. Reconfigurable networks are also compared with various other models of parallel computation, like PRAM's and Branching Programs. Part of this work is to be presented at the 18th International Colloquium on Automata, Languages, and Programming (ICALP), July 1991, Madrid. y Department of Computer Science, The Hebrew University, Jerusalem 91904, Israel. Email: yosi@humus.huji.ac.il, Supported by Eshcol Fellowship. z Department of Applied Mathematics and Computer Science, The Weizmann Institute, Rehovot 76100, Israel. Email: p...
The Computational Complexity of Universal Hashing
 Theoretical Computer Science
, 2002
"... Any implementation of CarterWegman universal hashing from nbit strings to mbit strings requires a timespace tradeoff of TS = Ω(nm). The bound holds in the general boolean branching program model, and thus in essentially any model of computation. As a corollary, computing a+b*c in any field ..."
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Cited by 59 (3 self)
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Any implementation of CarterWegman universal hashing from nbit strings to mbit strings requires a timespace tradeoff of TS = Ω(nm). The bound holds in the general boolean branching program model, and thus in essentially any model of computation. As a corollary, computing a+b*c in any field F requires a quadratic timespace tradeoff, and the bound holds for any representation of the elements of the field. Other lower bounds on the...
Analysis of Power Consumption on Switch Fabrics in Network Routers
 In Proc. Design Automation Conference
, 2002
"... In this paper, we introduce a framework to estimate the power consumption on switch fabrics in network routers. We propose different modeling methodologies for node switches, internal buffers and interconnect wires inside switch fabric architectures. A simulation platform is also implemented to trac ..."
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Cited by 58 (6 self)
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In this paper, we introduce a framework to estimate the power consumption on switch fabrics in network routers. We propose different modeling methodologies for node switches, internal buffers and interconnect wires inside switch fabric architectures. A simulation platform is also implemented to trace the dynamic power consumption with bitlevel accuracy. Using this framework, four switch fabric architectures are analyzed under different traffic throughput and different numbers of ingress/egress ports. This framework and analysis can be applied to the architectural exploration for low power high performance network router designs.
Randomized Routing on FatTrees
 Advances in Computing Research
, 1996
"... Fattrees are a class of routing networks for hardwareefficient parallel computation. This paper presents a randomized algorithm for routing messages on a fattree. The quality of the algorithm is measured in terms of the load factor of a set of messages to be routed, which is a lower bound on the ..."
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Cited by 51 (11 self)
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Fattrees are a class of routing networks for hardwareefficient parallel computation. This paper presents a randomized algorithm for routing messages on a fattree. The quality of the algorithm is measured in terms of the load factor of a set of messages to be routed, which is a lower bound on the time required to deliver the messages. We show that if a set of messages has load factor on a fattree with n processors, the number of delivery cycles (routing attempts) that the algorithm requires is O(+lg n lg lg n) with probability 1 \Gamma O(1=n). The best previous bound was O( lg n) for the offline problem in which the set of messages is known in advance. In the context of a VLSI model that equates hardware cost with physical volume, the routing algorithm can be used to demonstrate that fattrees are universal routing networks. Specifically, we prove that any routing network can be efficiently simulated by a fattree of comparable hardware cost. 1 Introduction Fattrees constitute...
Embedding graphs in books: a layout problem with applications to VLSI design
 SIAM J. ALGEBRAIC DISCRETE METHODS
, 1987
"... We study the graphtheoretic problem of embedding a graph in a book with its vertices in a line along the spine of the book and its edges on the pages in such a way that edges residing on the same page do not cross. This problem abstracts layout problems arising in the routing of multilayer printed ..."
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Cited by 48 (0 self)
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We study the graphtheoretic problem of embedding a graph in a book with its vertices in a line along the spine of the book and its edges on the pages in such a way that edges residing on the same page do not cross. This problem abstracts layout problems arising in the routing of multilayer printed circuit boards and in the design of faulttolerant processor arrays. In devising an embedding, one strives to minimize both the number of pages used and the "cutwidth" of the edges on each page. Our main results (1) present optimal embeddings of a variety of families of graphs; (2) exhibit situations where one can achieve small pagenumber only at the expense of large cutwidth; and (3) establish bounds on the minimum pagenumber of a graph based on various structural properties of the graph. Notable in the last category are proofs that (a) every nvertex dvalent graph can be embedded using O(dn1/2) pages, and (b) for every d>2 and all large n, there are nvertex dvalent graphs whose pagenumber is at least log n]"