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Computer Science: Faculty Publications and Other Works

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Full-Text Articles in VLSI and Circuits, Embedded and Hardware Systems

On The Area Of Hypercube Layouts, Ronald I. Greenberg, Lee Guan Sep 2002

On The Area Of Hypercube Layouts, Ronald I. Greenberg, Lee Guan

Computer Science: Faculty Publications and Other Works

This paper precisely analyzes the wire density and required area in standard styles for the hypercube. It shows that the most natural, regular layout of a hypercube of N^2 nodes in the plane, in a NxN grid arrangement, uses floor(2N/3)+1 horizontal wiring tracks for each row of nodes. (In the process, we see that the number of tracks per row can be reduced by 1 with a less regular design, as can also be seen from an independent argument of Bezrukov et al.) This paper also gives a simple formula for the wire density at any cut position and a …

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Minimizing Channel Density With Movable Terminals, Ronald I. Greenberg, Jau-Der Shih Feb 1997

Minimizing Channel Density With Movable Terminals, Ronald I. Greenberg, Jau-Der Shih

Computer Science: Faculty Publications and Other Works

We give algorithms to minimize density for VLSI channel routing problems with terminals that are movable subject to certain constraints. The main cases considered are channels with linear order constraints, channels with linear order constraints and separation constraints, channels with movable modules containing fixed terminals, and channels with movable modules and terminals. In each case, we improve previous results for running time and space by a factor of L/\lgn and L, respectively, where L is the channel length, and n is the number of terminals.

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Parallel Algorithms For Single-Layer Channel Routing, Ronald I. Greenberg, Shih-Chuan Hung, Jau-Der Shih Jan 1997

Parallel Algorithms For Single-Layer Channel Routing, Ronald I. Greenberg, Shih-Chuan Hung, Jau-Der Shih

Computer Science: Faculty Publications and Other Works

We provide efficient parallel algorithms for the minimum separation, offset range, and optimal offset problems for single-layer channel routing. We consider all the variations of these problems that are known to have linear- time sequential solutions rather than limiting attention to the "river-routing" context, where single-sided connections are disallowed. For the minimum separation problem, we obtain O(lgN) time on a CREW PRAM or O(lgN / lglgN) time on a (common) CRCW PRAM, both with optimal work (processor- time product) of O(N), where N is the number of terminals. For the offset range problem, we obtain the same time and processor …

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An Empirical Comparison Of Area-Universal And Other Parallel Computing Networks, Ronald I. Greenberg, Lee Guan Sep 1996

An Empirical Comparison Of Area-Universal And Other Parallel Computing Networks, Ronald I. Greenberg, Lee Guan

Computer Science: Faculty Publications and Other Works

This paper provides empirical comparison of the communication capabilities of two area-universal networks, the fat-tree and the fat-pyramid, to the popular mesh and hypercube networks for parallel computation. While area-universal networks have been proven capable of simulating, with modest slowdown, any computation of any other network of comparable area, prior work has generally left open the question of how area-universal networks compare to other networks in practice. Comparisons are performed using techniques of throughput and latency analysis that have previously been applied to k-ary n-cube networks and using various existing models to equate the hardware cost of the networks being …

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Single-Layer Channel Routing And Placement With Single-Sided Nets, Ronald I. Greenberg, Jau-Der Shih Aug 1996

Single-Layer Channel Routing And Placement With Single-Sided Nets, Ronald I. Greenberg, Jau-Der Shih

Computer Science: Faculty Publications and Other Works

This paper considers the optimal offset, feasible offset, and optimal placement problems for a more general form of single-layer VLSI channel routing than has usually been considered in the past. Most prior works require that every net has exactly one terminal on each side of the channel. As long as only one side of the channel contains multiple terminals of the same net, we provide linear-time solutions to all three problems. Such results are implausible if the placement of terminals is entirely unrestricted; in fact, the size of the output for the feasible offset problem may be Ω(n^2). The linear-time …

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The Fat-Pyramid And Universal Parallel Computation Independent Of Wire Delay, Ronald I. Greenberg Dec 1994

The Fat-Pyramid And Universal Parallel Computation Independent Of Wire Delay, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

This paper shows that a fat-pyramid of area Θ(A) requires only O(log A) slowdown to simulate any competing network of area A under very general conditions. The result holds regardless of the processor size (amount of attached memory) and number of processors in the competing networks as long as the limitation on total area is met. Furthermore, the result is valid regardless of the relationship between wire length and wire delay. We especially focus on elimination of the common simplifying assumption that unit time suffices to traverse a wire regardless of its length, since the assumption becomes more and more …

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Parallel Algorithms For Single-Layer Channel Routing, Ronald I. Greenberg, Shih-Chuan Hung, Jau-Der Shih Dec 1993

Parallel Algorithms For Single-Layer Channel Routing, Ronald I. Greenberg, Shih-Chuan Hung, Jau-Der Shih

Computer Science: Faculty Publications and Other Works

We provide efficient parallel algorithms for the minimum separation, offset range, and optimal offset problems for single-layer channel routing. We consider all the variations of these problems that have linear-time sequential solutions rather than limiting attention to the ``river-routing'' context, where single-sided connections are disallowed. For the minimum separation problem, we obtain O(lgN) time on a CREW PRAM or O(lgN/lglgN) time on a CRCW PRAM, both with optimal work (processor-time product) of O(N), where N is the number of terminals. For the offset range problem, we obtain the same time and processor bounds as long as only one side of …

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Feasible Offset And Optimal Offset For Single-Layer Channel Routing, Ronald I. Greenberg, Jau-Der Shih Jun 1993

Feasible Offset And Optimal Offset For Single-Layer Channel Routing, Ronald I. Greenberg, Jau-Der Shih

Computer Science: Faculty Publications and Other Works

The paper provides an efficient method to find all feasible offsets for a given separation in a VLSI channel routing problem in one layer. The prior literature considers this task only for problems with no single-sided nets. When single-sided nets are included, the worst-case solution time increases from Theta(n) to Omega(n^2), where n is the number of nets. But, if the number of columns c is O(n), one can solve the problem in time O(n^{1.5}lg n ), which improves upon a `naive' O(cn) approach. As a corollary of this result, the same time bound suffices to find the optimal offset …

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A Systolic Simulation And Transformation System, Ronald I. Greenberg, H.-C. Oh Mar 1993

A Systolic Simulation And Transformation System, Ronald I. Greenberg, H.-C. Oh

Computer Science: Faculty Publications and Other Works

This paper presents a CAD tool, SystSim, to ease the design of systolic systems. Given a high-level, functional description of processors, and a high-level description of their interconnection, SystSim will perform simulations and provide graphical output. SystSim will also perform transformations such as retiming, which eases use of the methodology of Leiserson and Saxe of designing a system with broadcasting and then obtaining a systolic system through retiming.

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Minimizing Channel Density With Movable Terminals, Ronald I. Greenberg, Jau-Der Shih Mar 1993

Minimizing Channel Density With Movable Terminals, Ronald I. Greenberg, Jau-Der Shih

Computer Science: Faculty Publications and Other Works

We give algorithms to minimize density for channels with terminals that are movable subject to certain constraints. The main cases considered are channels with linear order constraints, channels with linear order constraints and separation constraints, channels with movable modules containing fixed terminals, and channels with movable modules and terminals. In each case, previous results for running time and space are improved by a factor of L/lg n and L , respectively, where L is the channel length and n is the number of terminals.

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On The Difficulty Of Manhattan Channel Routing, Ronald I. Greenberg, Joseph Jaja, Sridhar Krishnamurthy Dec 1992

On The Difficulty Of Manhattan Channel Routing, Ronald I. Greenberg, Joseph Jaja, Sridhar Krishnamurthy

Computer Science: Faculty Publications and Other Works

We show that channel routing in the Manhattan model remains difficult even when all nets are single-sided. Given a set of n single-sided nets, we consider the problem of determining the minimum number of tracks required to obtain a dogleg-free routing. In addition to showing that the decision version of the problem isNP-complete, we show that there are problems requiring at least d+Omega(sqrt(n)) tracks, where d is the density. This existential lower bound does not follow from any of the known lower bounds in the literature.

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Minimum Separation For Single-Layer Channel Routing, Ronald I. Greenberg, F. Miller Maley Sep 1992

Minimum Separation For Single-Layer Channel Routing, Ronald I. Greenberg, F. Miller Maley

Computer Science: Faculty Publications and Other Works

We present a linear-time algorithm for determining the minimum height of a single-layer routing channel. The algorithm handles single-sided connections and multiterminal nets. It yields a simple routability test for single-layer switchboxes, correcting an error in the literature.

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Finding A Maximum-Density Planar Subset Of A Set Of Nets In A Channel, Ronald I. Greenberg, Jau-Der Shih Feb 1992

Finding A Maximum-Density Planar Subset Of A Set Of Nets In A Channel, Ronald I. Greenberg, Jau-Der Shih

Computer Science: Faculty Publications and Other Works

We present efficient algorithms to find a maximum-density planar subset of n 2-pin nets in a channel. The simplest approach is to make repeated usage of Supowit's dynamic programming algorithm for finding a maximum-size planar subset, which leads to O(n^3) time to find a maximum-density planar subset. But we also provide an algorithm whose running time is dependent on other problem parameters and is often more efficient. A simple bound on the running time of this algorithm is O(nlgn+n(t+1)w), where t is the number of two-sided nets, and w is the number of nets in the output. Though the worst-case …

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Efficient Interconnection Schemes For Vlsi And Parallel Computation, Ronald I. Greenberg Sep 1989

Efficient Interconnection Schemes For Vlsi And Parallel Computation, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

This thesis is primarily concerned with two problems of interconnecting components in VLSI technologies. In the first case, the goal is to construct efficient interconnection networks for general-purpose parallel computers. The second problem is a more specialized problem in the design of VLSI chips, namely multilayer channel routing. In addition, a final part of this thesis provides lower bounds on the area required for VLSI implementations of finite-state machines. This thesis shows that networks based on Leiserson's fat-tree architecture are nearly as good as any network built in a comparable amount of physical space. It shows that these "universal" networks …

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Efficient Multi-Layer Channel Routing, Ronald I. Greenberg Apr 1989

Efficient Multi-Layer Channel Routing, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

No abstract provided.

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Lower Bounds On The Area Of Finite-State Machines, M. J. Foster, Ronald I. Greenberg Jan 1989

Lower Bounds On The Area Of Finite-State Machines, M. J. Foster, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

There are certain straightforward algorithms for laying out finite-state machines. This paper shows that these algorithm are optimal in the worst case for machines with fixed alphabets. That is, for any s and k, there is a deterministic finite-state machine with s states and k symbols such that any layout algorithm requires Ω(ks log s) area to lay out its realization. Similarly, any layout algorithm requires Ω(ks^2) area in the worst case for nondeterministic finite-state machines with s states and k symbols.

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Randomized Routing On Fat-Trees, Ronald I. Greenberg, Charles E. Leiserson Jan 1989

Randomized Routing On Fat-Trees, Ronald I. Greenberg, Charles E. Leiserson

Computer Science: Faculty Publications and Other Works

Fat-trees are a class of routing networks for hardware-efficient parallel computation. This paper presents a randomized algorithm for routing messages on a fat-tree. 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 lambda on a fat-tree with n processors, the number of delivery cycles (routing attempts) that the algorithm requires is O(lambda + lg n lg lg n) with probability 1-O(1/n). The best previous …

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Mulch: A Multi-Layer Channel Router Using One, Two, And Three Layer Partitions, Ronald I. Greenberg, Alex T. Ishii, Alberto L. Sangiovanni-Vincentelli Nov 1988

Mulch: A Multi-Layer Channel Router Using One, Two, And Three Layer Partitions, Ronald I. Greenberg, Alex T. Ishii, Alberto L. Sangiovanni-Vincentelli

Computer Science: Faculty Publications and Other Works

Chameleon, a channel router for three layers of interconnect, has been implemented to accept specification of an arbitrary number of layers. Chameleon is based on a strategy of decomposing the multilayer problem into two- and three-layer problems in which one of the layers is reserved primarily for vertical wire runs and the other layer(s) for horizontal runs. In some situations, however, it is advantageous to consider also layers that allow the routing of entire nets, using both horizontal and vertical wires. MulCh is a multilayer channel router that extends the algorithms of Chameleon in this direction. MulCh can route channels …

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Randomized Routing On Fat-Trees, Ronald I. Greenberg Oct 1985

Randomized Routing On Fat-Trees, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

Fat-trees are a class of routing networks for hardware-efficient parallel computation. This paper presents a randomized algorithm for routing messages on a fat-tree. 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 lambda on a fat-tree with n processors, the number of delivery cycles (routing attempts) that the algorithm requires is O(lambda+lgnlglgn) with probability 1-O(1/ …

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