Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Engineering (17)
- Electrical and Computer Engineering (16)
- VLSI and Circuits, Embedded and Hardware Systems (16)
- OS and Networks (4)
- Computer Engineering (2)
-
- Computer and Systems Architecture (2)
- Bioinformatics (1)
- Discrete Mathematics and Combinatorics (1)
- Life Sciences (1)
- Mathematics (1)
- Operations Research, Systems Engineering and Industrial Engineering (1)
- Other Computer Sciences (1)
- Other Operations Research, Systems Engineering and Industrial Engineering (1)
- Probability (1)
- Statistics and Probability (1)
- Systems Architecture (1)
- Keyword
-
- Computer science (5)
- Area-universal networks (4)
- Channel routing (4)
- Randomized routing (4)
- Parallel computation (3)
-
- Wormhole routing (3)
- Fat-trees (2)
- Greedy routing (2)
- Interconnection networks (2)
- Layout algorithms (2)
- Lower bounds (2)
- Packet routing (2)
- Single-layer channel routing (2)
- Single-layer routing (2)
- VLSI (2)
- VLSI layout (2)
- Algorithms (1)
- Analysis of algorithms (1)
- Area-universality (1)
- Bijections (1)
- Bioinformatics (1)
- Biomolecular sequence analysis (1)
- Butterfly fat-tree (1)
- Combinatorial problems (1)
- Computational complexity (1)
- Computational thinking (1)
- Computer science education (1)
- Computing (1)
- Counting principles (1)
- Custom VLSI (1)
Articles 1 - 22 of 22
Full-Text Articles in Theory and Algorithms
Randomized Routing On Fat-Trees, Ronald I. Greenberg, Charles E. Leiserson
Randomized Routing On Fat-Trees, Ronald I. Greenberg, Charles E. Leiserson
Ronald Greenberg
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 …
Universal Wormhole Routing, Ronald I. Greenberg, Hyeong-Cheol Oh
Universal Wormhole Routing, Ronald I. Greenberg, Hyeong-Cheol Oh
Ronald Greenberg
We examine the wormhole routing problem in terms of the "congestion" c and "dilation" d for a set of packet paths. We show, with mild restrictions, that there is a simple randomized algorithm for routing any set of P packets in O(cdη + cLηlog P) time, where L is the number of flits in a packet, and η = min {d,L]; only a constant number of flits are stored in each queue at any time. Using this result, we show that a fat-tree network of area Θ(A) can simulate wormhole routing on any network of comparable area with O(log 3 …
The Fat-Pyramid And Universal Parallel Computation Independent Of Wire Delay, Ronald I. Greenberg
The Fat-Pyramid And Universal Parallel Computation Independent Of Wire Delay, Ronald I. Greenberg
Ronald Greenberg
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 …
Randomized Routing On Fat-Trees, Ronald I. Greenberg
Randomized Routing On Fat-Trees, Ronald I. Greenberg
Ronald Greenberg
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/ …
Universal Wormhole Routing, Ronald I. Greenberg, Hyeong-Cheol Oh
Universal Wormhole Routing, Ronald I. Greenberg, Hyeong-Cheol Oh
Ronald Greenberg
In this paper, we examine the wormhole routing problem in terms of the “congestion” c and “dilation” d for a set of packet paths. We show, with mild restrictions, that there is a simple randomized algorithm for routing any set of P packets in O(cdη+cLηlogP) time with high probability, where L is the number of flits in a packet, and η=min{d,L}; only a constant number of flits are stored in each queue at any time. Using this result, we show that a fat-tree network of area Θ(A) can simulate wormhole routing on any network of comparable area with O(log^3 A) …
Single-Layer Channel Routing And Placement With Single-Sided Nets, Ronald I. Greenberg, Jau-Der Shih
Single-Layer Channel Routing And Placement With Single-Sided Nets, Ronald I. Greenberg, Jau-Der Shih
Ronald Greenberg
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 …
On The Difficulty Of Manhattan Channel Routing, Ronald I. Greenberg, Joseph Jaja, Sridhar Krishnamurthy
On The Difficulty Of Manhattan Channel Routing, Ronald I. Greenberg, Joseph Jaja, Sridhar Krishnamurthy
Ronald Greenberg
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.
On The Area Of Hypercube Layouts, Ronald I. Greenberg, Lee Guan
On The Area Of Hypercube Layouts, Ronald I. Greenberg, Lee Guan
Ronald Greenberg
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 …
Minimizing Channel Density With Movable Terminals, Ronald I. Greenberg, Jau-Der Shih
Minimizing Channel Density With Movable Terminals, Ronald I. Greenberg, Jau-Der Shih
Ronald Greenberg
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.
Minimizing Channel Density With Movable Terminals, Ronald I. Greenberg, Jau-Der Shih
Minimizing Channel Density With Movable Terminals, Ronald I. Greenberg, Jau-Der Shih
Ronald Greenberg
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.
Parallel Algorithms For Single-Layer Channel Routing, Ronald I. Greenberg, Shih-Chuan Hung, Jau-Der Shih
Parallel Algorithms For Single-Layer Channel Routing, Ronald I. Greenberg, Shih-Chuan Hung, Jau-Der Shih
Ronald Greenberg
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 …
Parallel Algorithms For Single-Layer Channel Routing, Ronald I. Greenberg, Shih-Chuan Hung, Jau-Der Shih
Parallel Algorithms For Single-Layer Channel Routing, Ronald I. Greenberg, Shih-Chuan Hung, Jau-Der Shih
Ronald Greenberg
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 …
Packet Routing In Networks With Long Wires, Ronald I. Greenberg, Hyeong-Cheol Oh
Packet Routing In Networks With Long Wires, Ronald I. Greenberg, Hyeong-Cheol Oh
Ronald Greenberg
In this paper, we examine the packet routing problem for networks with wires of differing length. We consider this problem in a network independent context, in which routing time is expressed in terms of "congestion" and "dilation" measures for a set of packet paths. We give, for any constant ϵ > 0, a randomized on-line algorithm for routing any set of Npackets in O((C lgϵ(Nd) + D lg(Nd))/lg lg(Nd)) time, where C is the maximum congestion and D is the length of the longest path, both taking wire delays into …
Finding Connected Components On A Scan Line Array Processor, Ronald I. Greenberg
Finding Connected Components On A Scan Line Array Processor, Ronald I. Greenberg
Ronald Greenberg
This paper provides a new approach to labeling the connected components of an n x n image on a scan line array processor (comprised of n processing elements). Variations of this approach yield an algorithm guaranteed to complete in o(n lg n) time as well as algorithms likely to approach O(n) time for all or most images. The best previous solutions require using a more complicated architecture or require Omega(n lg n) time. We also show that on a restricted version of the architecture, any algorithm requires Omega(n lg n) time in the worst case.
Feasible Offset And Optimal Offset For Single-Layer Channel Routing, Ronald I. Greenberg, Jau-Der Shih
Feasible Offset And Optimal Offset For Single-Layer Channel Routing, Ronald I. Greenberg, Jau-Der Shih
Ronald Greenberg
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 …
Fast And Space-Efficient Location Of Heavy Or Dense Segments In Run-Length Encoded Sequences, Ronald I. Greenberg
Fast And Space-Efficient Location Of Heavy Or Dense Segments In Run-Length Encoded Sequences, Ronald I. Greenberg
Ronald Greenberg
This paper considers several variations of an optimization problem with potential applications in such areas as biomolecular sequence analysis and image processing. Given a sequence of items, each with a weight and a length, the goal is to find a subsequence of consecutive items of optimal value, where value is either total weight or total weight divided by total length. There may also be a specified lower and/or upper bound on the acceptable length of subsequences. This paper shows that all the variations of the problem are solvable in linear time and space even with non-uniform item lengths and divisible …
Lower Bounds On The Area Of Finite-State Machines, M. J. Foster, Ronald I. Greenberg
Lower Bounds On The Area Of Finite-State Machines, M. J. Foster, Ronald I. Greenberg
Ronald Greenberg
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.
Efficient Multi-Layer Channel Routing, Ronald I. Greenberg
Efficient Multi-Layer Channel Routing, Ronald I. Greenberg
Ronald Greenberg
No abstract provided.
Finding A Maximum-Denisty Planar Subset Of A Set Of Nets In A Channel, Ronald I. Greenberg, Jau-Der Shih
Finding A Maximum-Denisty Planar Subset Of A Set Of Nets In A Channel, Ronald I. Greenberg, Jau-Der Shih
Ronald Greenberg
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 …
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Ronald Greenberg
Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.
Efficient Interconnection Schemes For Vlsi And Parallel Computation, Ronald I. Greenberg
Efficient Interconnection Schemes For Vlsi And Parallel Computation, Ronald I. Greenberg
Ronald Greenberg
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 …
An Improved Analytical Model For Wormhole Routed Networks With Application To Butterfly Fat-Trees, Ronald I. Greenberg, Lee Guan
An Improved Analytical Model For Wormhole Routed Networks With Application To Butterfly Fat-Trees, Ronald I. Greenberg, Lee Guan
Ronald Greenberg
A performance model for wormhole routed interconnection networks is presented and applied to the butterfly fat-tree network. Experimental results agree very closely over a wide range of load rate. Novel aspects of the model, leading to accurate and simple performance predictions, include (1) use of multiple-server queues, and (2) a general method of correcting queuing results based on Poisson arrivals to apply to wormhole routing. These ideas can also be applied to other networks.