Introduction To State Estimation Of High-Rate System Dynamics, 2018 Iowa State University

#### Introduction To State Estimation Of High-Rate System Dynamics, Jonathan Hong, Simon Laflamme, Jacob Dodson, Bryan Joyce

*Civil, Construction and Environmental Engineering Publications*

Engineering systems experiencing high-rate dynamic events, including airbags, debris detection, and active blast protection systems, could benefit from real-time observability for enhanced performance. However, the task of high-rate state estimation is challenging, in particular for real-time applications where the rate of the observer’s convergence needs to be in the microsecond range. This paper identifies the challenges of state estimation of high-rate systems and discusses the fundamental characteristics of high-rate systems. A survey of applications and methods for estimators that have the potential to produce accurate estimations for a complex system experiencing highly dynamic events is presented. It is argued ...

Randomized Routing On Fat-Trees, 2018 Loyola University Chicago

#### 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 ...

The Fat-Pyramid And Universal Parallel Computation Independent Of Wire Delay, 2018 Loyola University Chicago

#### 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 ...

Randomized Routing On Fat-Trees, 2018 Selected Works

#### 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*+lg*n*lglg*n*) with probability 1-*O*(1/*n*). The ...

Universal Wormhole Routing, 2018 Selected Works

#### 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 ...

Single-Layer Channel Routing And Placement With Single-Sided Nets, 2018 Selected Works

#### 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 ...

On The Difficulty Of Manhattan Channel Routing, 2018 Loyola University Chicago

#### 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, 2018 Selected Works

#### 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 ...

Minimum Separation For Single-Layer Channel Routing, 2018 Loyola University Chicago

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

*Ronald Greenberg*

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.

Mulch: A Multi-Layer Channel Router Using One, Two, And Three Layer Partitions, 2018 Loyola University Chicago

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

*Ronald Greenberg*

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 ...

Minimizing Channel Density With Movable Terminals, 2018 Loyola University Chicago

#### 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, 2018 Selected Works

#### 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, 2018 Selected Works

#### 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 ...

Parallel Algorithms For Single-Layer Channel Routing, 2018 Selected Works

#### 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 ...

Feasible Offset And Optimal Offset For Single-Layer Channel Routing, 2018 Loyola University Chicago

#### 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 ...

Lower Bounds On The Area Of Finite-State Machines, 2018 Loyola University Chicago

#### 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, 2018 Selected Works

#### 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, 2018 Selected Works

#### 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 ...

Efficient Interconnection Schemes For Vlsi And Parallel Computation, 2018 Loyola University Chicago

#### 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 ...

An Empirical Comparison Of Area-Universal And Other Parallel Computing Networks, 2018 Selected Works

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

*Ronald Greenberg*

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 ...