Efficient Deterministic and Probabilistic Simulations of PRAMs on Linear Arrays with Reconfigurable Pipelined Bus Systems

In the channel routing problem, terminals between cells are interconnected completely while reducing channel routing area. The crossing number, the number of crossings between two wires in the channel, is related to the channel routing area. In this paper, we present a parallel algorithm finding a maximum crossing number, density, in the channel by using a LARPBS model (Linear Array with a Reconfigurable Pipelined Bus System), which is based on the advanced fiber optic technology. The maximum crossing number algorithm on the LARPBS model runs in O(n) time using O(n) number of processors, where n is the number of nets in a channel.

We present efficient parallel matrix multiplication algorithms for linear arrays with reconfigurable pipelined bus systems (LARPBS). Such systems are able to support a large volume of parallel communication of various patterns in constant time. An LARPBS can also be reconfigured into many independent subsystems and, thus, is able to support parallel implementations of divide-and-conquer computations like Strassen's algorithm. The main contributions of the paper are as follows. We develop five matrix multiplication algorithms with varying degrees of parallelism on the LARPBS computing model; namely, MM/sub 1/, MM/sub 2/, MM/sub 3/, and compound algorithms C/sub 1/(/spl epsiv/)and C/sub 2/(/spl delta/). Algorithm C/sub 1/(/spl epsiv/) has adjustable time complexity in sublinear level. Algorithm C/sub 2/(/spl delta/) implies that it is feasible to achieve sublogarithmic time using /spl sigma/(N/sup 3/) processors for matrix multiplication on a realistic system. Algorithms MM/sub 3/, C/sub 1/(/spl epsiv/), and C/sub 2/(/spl delta/) all have o(/spl Nscr//sup 3/) cost and, hence, are very processor efficient. Algorithms MM/sub 1/, MM/sub 3/, and C/sub 1/(/spl epsiv/) are general-purpose matrix multiplication algorithms, where the array elements are in any ring. Algorithms MM/sub 2/ and C/sub 2/(/spl delta/) are applicable to array elements that are integers of bounded magnitude, or floating-point values of bounded precision and magnitude, or Boolean values. Extension of algorithms MM/sub 2/ and C/sub 2/(/spl delta/) to unbounded integers and reals are also discussed.

We present two fast algorithms for sorting on a linear array with a reconfigurable pipelined bus system (LARPBS), one of the recently proposed parallel architectures based on optical buses. In our first algorithm, we sort N numbers in O(log N log log N) worst-case time using N processors. In our second algorithm, we sort N numbers in O((log log N)/sup 2/) worst-case time using N/sup 1+/spl epsi// processors, for any fixed /spl epsi/ such that 0 < /spl epsi/ < 1. Our algorithms are based on a novel deterministic sampling scheme for merging two sorted arrays of length N each in O(log log N) time on an LARPBS with N processors. To our knowledge, the previous best sorting algorithm on this architecture has a running time of O((log N)/sup 2/) using N processors.

In this paper, we present an efficient deterministic algorithm for sorting on the LARPBS (Linear Array with a Reconfigurable Pipelined Optical Bus System) model. Our sorting algorithm sorts n general keys in O(logn) time on a LARPBS of size nslogn. The previous best results can sort n items in O(lognloglogn) worst-case time using n processors or sort n items in O((log logn2)worst-case time using n1+ processors. Our algorithm is also scalable to certain extent. When the system size is reduced to nslogn/r for l≤r≤logn, the total computation time is O(rlogn).

We present a fast algorithm for sorting on a linear array with a reconfigurable pipelined bus system (LARPBS), one of the recently proposed parallel architectures based on optical buses. Our algorithm sorts N numbers in O(log N log logN) worst-case time using N processors. To our knowledge, the previous best sorting algorithm on this architecture has a running time of O(log2N).KeywordsLinear ArrayRecursive CallSorting AlgorithmMerging AlgorithmDestination ProcessorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The optical bus based arrays have recently shown many applications. In this paper we use the pipelining ability of the LARPBS to solve the repetitions detection problem. We propose an algorithm that finds all kind of repetitions in a string including k-power repetitions, overlapping repetitions and non-contiguous repetitions. For a given distance, this operation is performed in O(1) communication cycle with a constant computation time processors on a O(n) processors LARPBS for a string of length n. For all the periods, it is O(n) bus cycle. No previous algorithms were known for this problem on the LARPBS.

Almost all of the existing two-dimensional block-based medial axis transform (2D_BB_MAT) parallel algorithm are devised for solving the 2D_BB_MAT problem only and are very difficult to extend to a solution of the 3D_BB_MAT problem in parallel. In this paper, we propose efficient O(1) time algorithms for solving the hD_BB_MAT problems, where h is 2 or 3, on the linear array with a reconfigurable pipelined bus system (LARPBS) model. The proposed 2D_BB_MAT algorithm can easily extend to a solution of the 3D_BB_MAT problem in parallel by reducing the hD_BB_MAT problems to the forward chessboard distance transform problems. To the best of our knowledge, the proposed algorithms are the most efficient O(1) time algorithms compared with all the previously published algorithms known.

Efficient and scalable quicksort on a linear array with a reconfigurable pipelined bus system

Information gap decision theory with risk aversion strategy for robust planning of hybrid photovoltaic/wind/battery storage system in distribution networks considering uncertainty

Field-Programmable Gate Arrays (FPGAs) have become an attractive option for scientific computing. Several vendors have developed high performance reconfigurable systems which employ FPGAs for application acceleration. In this paper, we propose a BLAS (Basic Linear Algebra Subprograms) library for state-of-the-art reconfigurable systems. We study three data-intensive operations: dot product, matrix-vector multiply and dense matrix multiply. The first two operations are I/O bound, and our designs efficiently utilize the available memory bandwidth in the systems. As these operations require accumulation of sequentially delivered floating-point values, we develop a high performance reduction circuit. This circuit uses only one floating-point adder and buffers of moderate size. For matrix multiply operation, we propose a design which employs a linear array of FPGAs. This design exploits the memory hierarchy in the reconfigurable systems, and has very low memory bandwidth requirements. To illustrate our ideas, we have implemented our designs for Level 2 and Level 3 BLAS on Cray XD1.

The Federal Government of Nigeria intends to develop the domestic gas market by opening investment opportunity for infrastructural development, and by including gas pipeline construction among her key projects in 2009 budget. The domestic gas market is estimated to have an annual growth potential of about 15% to 18%, which attests to its potential profitability. In this study, we investigated the gas transmission tariff and profitability potential for investment in the gas transmission investment opportunity proposed in the Nigerian Gas Master Plan. The gas transmission systems are the South-North System, the Western System, and the Interconnector System. Deterministic and stochastic methods were used for cashflow modeling and sensitivity analysis. Using 17% internal rate of returns, the resulting tariffs for the gas transmission systems were the following: $0.47/Mscf for the Western Pipeline System, $0.97/MScf for South-North pipeline system, and $0.34/MScf for Interconnector pipeline system. The most sensitive cost items to internal rate of returns for investment in the pipeline systems were determined as the peak flow of gas, gas pipeline costs, and installation costs. The calculated tariffs could be coupled with the casing head gas price and processing fee to yield the likely price of the lean gas.

Recently, wireless channel in vehicle-to-vehicle (V2V) communications is highly challenging due to rapid signal fluctuations, multi-path fading, and frequent obstructions. To mitigate these issues, this paper proposes a three-dimensional (3D) end-to-end channel model for reconfigurable intelligent surface (RIS)-assisted V2V wireless channels. The proposed channel model incorporates the motions of the mobile transmitter (MT), mobile receiver (MR), and a UAV-mounted RIS, capturing time-varying propagation characteristics. Key contributions include the derivation of exact analytical expressions for the level crossing rate (LCR) of the Rician fading envelope, along with efficient deterministic and stochastic simulation methods. Numerical results analyze the impact of RIS motion direction and scatterer distribution on the LCR, providing theoretical insights for optimizing RIS-assisted V2V systems in wireless communication environments.

In this theoretical study of epileptiform activity, the onset of self-sustained activity in a system of interconnected cells is explored using (a) analytical models, and (b) computer simulations. An approximate analytical model demonstrates that the system can be either stable, with self-sustained activity impossible, or potentially unstable, with the possibility of going into self-sustained activity if the firing rate is driven beyond a critical level. The approximations made in this initial model led to substantial discrepancies when the analytical criticality condition was tested against computer simulations in relatively small networks of neurons. Therefore, using a refined analytical model, a numerically more accurate, although computationally cumbersome, criticality condition was derived which agrees well with the simulation results. Two simulation models are used: a deterministic simulation in which the average number of cells firing at each simulation step is calculated and a probabilistic simulation in which the stimulation and firing of each individual neuron is followed. Comparison between the behavior of the probabilistic and deterministic simulations near criticality demonstrates that random fluctuations can force the system toward either self-sustained activity or decay.

Stability analyses of geotechnical structures in rock are traditionally performed using deterministic methods. In Europe, Eurocode7, introduced in the beginning of the 21st century, adopts limit state design and semi-probabilistic methods, using partial factors for the design of geotechnical structures. Meanwhile, reliability-based design, using probabilistic methods, is becoming more common in practical cases. The paper considers an intentionally simple case study—the analysis of a slope in a rock mass with one discontinuity, considered in a discrete way, forming a rock block to be stabilised by anchors—to compare the results obtained with the different methods. The objective is to calculate the force applied by the anchors so that the ultimate limit states of sliding of the rock block is verified. Deterministic-based design optimization considering both the traditional global safety factor approach and the partial factor approach following the Eurocode 7 are first applied. A reliability-based design optimization procedure—which takes geometrical and mechanical properties of the discontinuities as random variables—is then used, and the results are compared to the former ones. A discussion is presented concerning the consistency of the obtained results.

Monte Carlo simulation is widely used in pricing and risk management of complex financial instruments. Deterministic simulation methods (quasi-Monte Carlo methods) are superior to Monte Carlo in terms of accuracy and speed. The authors show how deterministic simulation can be applied to calculate value at risk. They use in their tests a portfolio of collaterized mortgage obligation tranches. One of the deterministic methods consistently outperforms Monte Carlo simulation.