Reconfigurable Pipelined Bus System Research Articles

Optical Pipelined Multi-bus Interconnection Network Intrinsic Topologies

Digital all-optical parallel computing is an important research direction and spans conventional devices and convergent nano-optics deployments. Optical bus-based interconnects provide interesting aspects such as relative information communication speed-up or slow-down between optical signals. This aspect is harnessed in the newly proposed All-Optical Linear Array with a Reconfigurable Pipelined Bus System (OLARPBS) model. However, the physical realization of such communication interconnects needs to be considered. This paper considers spatial layouts of processing elements along with the optical bus light paths that are necessary to realize the corresponding interconnection requirements. A metric in terms of the degree of required physical constraint is developed to characterize the variety of possible solutions. Simple algorithms that determine spatial layouts are given. It is shown that certain communication interconnection structures have associated intrinsic topologies.

High-bandwidth flexible interconnections in the all-optical linear array with a reconfigurable pipelined bus system (OLARPBS) optical conduit parallel computing model

The all-optical linear array with a reconfigurable pipelined bus system (OLARPBS) optical conduit parallel computing model consists of pipelined optical conduits (buses) that interconnect all-optical processing elements. Previous work on the OLARPBS, following the designs of predecessor models, considered interconnections that mostly, rigidly connected a linear array of processing elements in the same specific order. Such rigidness results in a communication (memory) bound architecture and imposes algorithm scheduling difficulties, both of which potentially limit the capability of the model. A highly scalable and flexible interconnect, designed for high-bandwidth and high-speed interconnections, is developed in this paper. A matrix multiplication algorithm is designed to take advantage of this new interconnection design and includes a comparison with a previous algorithm. The advantages include addressing the communication limitations and enabling more flexible algorithms with increased processing efficiency.

All-optical Linear Array with a Reconfigurable Pipelined Bus System (OLARPBS) optical bus parallel computing model

The All-optical Linear Array with a Reconfigurable Pipelined Bus System (OLARPBS) optical bus parallel computing model is proposed in this paper. The OLARPBS model includes several architectural an...

Optimal Sorting Algorithms for a Simplified 2D Array with Reconfigurable Pipelined Bus System

In recent years, many researchers have investigated optical interconnections as parallel computing. Optical interconnections are attractive due to their high bandwidth and concurrent access to the bus in a pipelined fashion. The Linear Array with Reconfigurable Pipelined Bus System (LARPBS) model is a powerful optical bus system that combines both the advantages of optical buses and reconfiguration. To increase the scalability of the LARPBS model, we propose a two-dimensional extension: a simplified two-dimensional Array with Reconfigurable Pipelined Bus System (2D ARPBS). While achieving better scalability, we show the effectiveness of this newly proposed model by designing two novel optimal sorting algorithms on this model. The first sorting algorithm is an extension of Leighton's seven-phase columnsort algorithm that eliminates the restriction of sorting only an r × s array, where r ? s2 , and sorts an n × n array in O(log n) time. The second one is an optimal multiway mergesort algorithm that uses a novel processor efficient two-way mergesort algorithm and a novel multiway merge scheme to sort n2 items in O(log n) time. Using an optimal sorting algorithm Pipelined Mergesort designed for the LARPBS model as a building block, we extend our research on parallel sorting on the LARPBS to a more scalable 2D ARPBS model and achieve optimality in both sorting algorithms.

An optical power budget model for the Parameterized Linear Array with a Reconfigurable Pipelined Bus System (LARPBS(p)) model

The Parameterized Linear Array with a Reconfigurable Pipelined Bus System (LARPBS(p)) model consists of a virtual machine architecture, routing and addressing, communication primitives and parameterization for algorithm cost and comparison. Unique features of this model over the earlier LARPBS model include its execution time parameterization of the model’s virtual machine abstraction as well as two new communication primitives. However, both models share similar architectures. A passive optical fiber-based implementation of the abstract machine architecture for the LARPBS(p) and LARPBS models is described. The feasibility of selected device implementation is assessed through the development of an optical power budget model that includes estimation for the signal loss, power budget, and the maximum number of supported processors. The model is applied to four case studies. Based on these case studies, a further scalability analysis is conducted. Lastly, comments are made about the achievable data rates while maintaining a low BER.

An optimal and processor efficient parallel sorting algorithm on a linear array with a reconfigurable pipelined bus system

Optical interconnections attract many engineers and scientists’ attention due to their potential for gigahertz transfer rates and concurrent access to the bus in a pipelined fashion. These unique characteristics of optical interconnections give us the opportunity to reconsider traditional algorithms designed for ideal parallel computing models, such as PRAMs. Since the PRAM model is far from practice, not all algorithms designed on this model can be implemented on a realistic parallel computing system. From this point of view, we study Cole’s pipelined merge sort [Cole R. Parallel merge sort. SIAM J Comput 1988;14:770–85] on the CREW PRAM and extend it in an innovative way to an optical interconnection model, the LARPBS (Linear Array with Reconfigurable Pipelined Bus System) model [Pan Y, Li K. Linear array with a reconfigurable pipelined bus system—concepts and applications. J Inform Sci 1998;106;237–58]. Although Cole’s algorithm is optimal, communication details have not been provided due to the fact that it is designed for a PRAM. We close this gap in our sorting algorithm on the LARPBS model and obtain an O(log N)-time optimal sorting algorithm using O( N) processors. This is a substantial improvement over the previous best sorting algorithm on the LARPBS model that runs in O(log N log log N) worst-case time using N processors [Datta A, Soundaralakshmi S, Owens R. Fast sorting algorithms on a linear array with a reconfigurable pipelined bus system. IEEE Trans Parallel Distribut Syst 2002;13(3):212–22]. Our solution allows efficiently assign and reuse processors. We also discover two new properties of Cole’s sorting algorithm that are presented as lemmas in this paper.

A novel [formula omitted] time algorithm for 3D block-based medial axis transform by peeling corner shells

The block-based medial axis transform ( BB_ MAT, for short) of a 3D (2D) binary image, denoted 3D_BB_MAT (2D_BB_MAT), is defined as the problem to find a minimal set of upright 1-cubes (1-squares) whose union corresponds exactly to the 1-voxels (1-pixels) in the binary image. Many parallel algorithms have been proposed for computing the 2D_BB_MAT, almost all proposed approaches are unable to extend to a solution of the 3D_BB_MAT problem. In this paper, we first propose a novel O ( 1 ) time algorithm for solving the 3D_BB_MAT (2D_BB_MAT) problem of a binary image of size N × N × N ( N × N ) on a linear array with a reconfigurable pipelined bus system ( LARPBS, for short) by peeling the 3D (2D) corner shell of each 1-voxel (1-pixel) of the image and revealing some properties of the 3D_BB_MAT (2D_BB_MAT). The 3D (2D) chessboard distance transform problem, denoted 3D_CDT (2D_CDT), is the problem for each 0-voxel (0-pixel) of a 3D (2D) binary image to find its nearest 1-voxel (1-pixel) in the binary image based on chessboard distance metric. In this paper, we also solve the 3D_CDT (2D_CDT) based on the computed 3D_BB_MAT (2D_BB_MAT). All the proposed algorithms are very innovative although they look like “straightforward”. To the best of our knowledge, the proposed 2D_BB_MAT (2D_CDT) algorithm is the first algorithm that can extend to a solution of the 3D_BB_MAT (3D_CDT) problem in parallel, and the 3D_BB_MAT (3D_CDT) algorithm is the first parallel algorithm proposed for solving the 3D_BB_MAT (3D_CDT) problem.

The systems edge of the Parameterized Linear Array with a Reconfigurable Pipelined Bus System (LARPBS(p)) optical bus parallel computing model

This paper is about exploring the various systems related aspects pertinent in the recent Parameterized Linear Array with a Reconfigurable Pipelined Bus System (LARPBS(p)) model. The two principal features of the LARPBS(p) model is, firstly, its bridging model definition similar to that of the BSP model leading to a more detailed algorithm cost analysis than other models, and secondly, the incorporation of several new communication primitives not defined in earlier models. This paper reviews the systems related aspects of earlier optical bus models and summarizes the LARPBS(p) model. The main part of this paper considers some practical systems related aspects of the LARPBS(p) model, specifically: fiber and free space based implementations, feasibility study, communication traffic analysis, bus collision avoidance, and the cost analysis of a MIMD algorithm. An overview perspective of the work is presented, thereby: the edge of systems related research is identified.

Parallel Algorithms for String Matching Problem on Single and Two Dimensional Reconfigurable Pipelined Bus Systems

We considered string matching on LARPBS and 2D LARPBS. This has applications such as string databases, cellular automata and computational biology. The main use of this method is to reduce the time spent on comparisons in string matching by using LARPBS. We investigated exact string matching and approximate string matching problems. For these two sub problems, we obtained O (n) bus cycles algorithm and constant bus cycles algorithm. These algorithms have some disadvantages: Reconnecting the sub buses and shuffling the contents .These problems can be solved by 2D LARPBS.

An efficient [formula omitted] time 3D all nearest neighbor algorithm from image processing perspective

In this paper, we solve the k-dimensional all nearest neighbor ( kD_ANN) problem, where k = 2 or 3, on a linear array with a reconfigurable pipelined bus system (LARPBS) from image processing perspective. First, for a two-dimensional (2D) binary image of size N × N , we devise an algorithm for solving the 2D_ANN problem using a LARPBS of size N 2 + ϵ , where 0 < ϵ ⪡ 1 . Then, for a three-dimensional (3D) binary image of size N × N × N , we devise an algorithm for solving the 3D_ANN problem using a LARPBS of size N 3 + ɛ , where 0 < ɛ < 1 . To the best of our knowledge, all results derived above are the best O ( 1 ) time 2D_ANN and 3D_ANN algorithms on the LARPBS model known.

Repetitions detection on a linear array with reconfigurable pipelined bus system

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.

Parallel algorithms for robot path planning with simpler VLSI architecture

This paper proposes a parallel algorithm for robot path planning on a linear array with a reconfigurable pipelined bus system (LARPBS) through the construction of a Voronoi diagram on a binary image of the workspace. The algorithm is based on a d4 distance metric, and it does not incur any additional time or processor requirements compared with those of a previously reported proposal (Tzionas et al., 1997). This paper recommends the same model as the simpler VLSI architecture for the problem in question.

Efficient algorithms for the all nearest neighbor and closest pair problems on the linear array with a reconfigurable pipelined bus system

We present two O(1)-time algorithms for solving the 2D all nearest neighbor (2D/spl I.bar/ANN) problem, the 2D closest pair (2D/spl I.bar/CP) problem, the 3D all nearest neighbor (3D/spl I.bar/ANN) problem and the 3D-closest pair (3D/spl I.bar/CP) problem of n points on the linear array with a reconfigurable pipelined bus system (LARPBS) from the computational geometry perspective. The first O(1) time algorithm, which invokes the ANN properties (introduced in this paper) only once, can solve the 2D/spl I.bar/ANN and 2D/spl I.bar/CP problems of n points on an LARPBS of size 1/2n/sup 5/3+c/, and the 3D/spl I.bar/ANN and 3D/spl I.bar/CP problems pf n points on an LARPBS of size 1/2n/sup 7/4+c/, where 0 < /spl epsi/ = 1/2/sup c+1/-1 /spl Lt/ 1, c is a constant and positive integer. The second O(1) time algorithm, which recursively invokes the ANN properties k times, can solve the kD/spl I.bar/ANN, and kD/spl I.bar/CP problems of n points on an LARPBS of size 1/2n/sup 3/2+c/, where k = 2 or 3, 0 < /spl epsi/ = 1/2/sup n+1/-1 /spl Lt/ 1, and c is a constant and positive integer. To the best of our knowledge, all results derived above are the best O(1) time ANN algorithms known.

Constant time fault tolerant algorithms for a linear array with a reconfigurable pipelined bus system

Recently, researchers have proposed many models using reconfigurable optically pipelined buses. Most algorithms developed for these models assume that a healthy system is available. The only previous work in this area considers faulty processors or hardware for an N-processor linear array with a reconfigurable pipelined bus system (LARPBS), resulting in fault tolerant algorithms that run in O ( log N ) time. We extend and improve upon previous results by considering new fault scenarios and slight modifications to the LARPBS model. By modifying the switches on the receiving segment of an LARPBS, a reasonable, low-cost extension to the model, we are able to achieve fault tolerant algorithms that execute in O ( 1 ) time rather than O ( log N ) time. The fault tolerant algorithms that we consider are key basic fundamental algorithms, such as compaction, binary prefix sums, and sorting, that all execute in constant time on a healthy LARPBS. As the algorithms improved are building blocks for more complex algorithms, the results presented in this paper will extend to those more complex algorithms as well.

A Parameterized Linear Array with a Reconfigurable Pipelined Bus System: LARPBS(p)

The linear array with a reconfigurable pipelined bus system (LARPBS) is an optical bus-based theoretical parallel computation model. Many parallel algorithms have been proposed using this model of computation. However, a current limitation of the LARPBS model is that it does not provide for performance prediction of these algorithms running on realistic implementations of the LARPBS model. This paper investigates the parameterization of the LARPBS model so as to overcome this limitation. Specifically, a new parameterized parallel computation model, the LARPBS(p) model, is proposed in this paper. The LARPBS(p) model captures computational costs through six abstract parameters: the number of processors, the communication latency, the communication overhead, the network capacity, the computation time and the synchronization time. The proposed parameters and, subsequently, the cost analysis on the LARPBS(p) model are presented. In addition applications of the cost analysis to some primitive operations and to two matrix multiplication algorithms on the LARPBS(p) are also presented. LARPBS(p) is intended to serve as a basis for a more accurate estimation of execution time of algorithms by providing greater detail of the costs involved on the LARPBS.

Fast and scalable parallel matrix computations with reconfigurable pipelined optical buses

We present fast and highly scalable parallel computations for a number of important and fundamental matrix problems on linear arrays with reconfigurable pipelined optical bus systems. These problems include computing the powers, the inverse, the characteristic polynomial, the determinant, the rank and an LU- and a QR-factorization of a matrix; multiplying a chain of matrices; and solving linear systems of equations. These computations are based on efficient implementation of the fastest sequential matrix multiplication algorithm, and are highly scalable over a wide range of system size. Such fast and scalable parallel matrix computations were not seen before on distributed memory parallel computing systems.

Multiple Addition and Prefix Sum on a Linear Array with a Reconfigurable Pipelined Bus System

We present several fast algorithms for multiple addition and prefix sum on the Linear Array with a Reconfigurable Pipelined Bus System (LARPBS), a recently proposed architecture based on optical buses. Our algorithm for adding N integers runs on an N log M-processor LARPBS in O(log* N) time, where log* N is the number of times logarithm has to be taken to reduce N below 1 and M is the largest integer in the input. Our addition algorithm improves the time complexity of several matrix multiplication algorithms proposed by Li, Pan and Zheng (IEEE Trans. Parallel and Distributed Systems, 9(8):705–720, 1998). We also present several fast algorithms for computing prefix sums of N integers on the LARPBS. For integers with bounded magnitude, our first algorithm for prefix sum computation runs in O(log log N) time using N processors and in O(1) time using N1+e processors, for \frac{1}{3} ≤ e < 1. For integers with unbounded magnitude, the first algorithm for multiple addition runs in O(log log N log* N) time using N log M processors, when M is the largest integer in the input. Our second algorithm for multiple addition runs in O(log* N) time using N1+e log M processors, for \frac {1}{3} ≤ e < 1. We also show suitable extensions of our algorithm for real numbers.

Fast and scalable algorithms for the Euclidean distance transform on a linear array with a reconfigurable pipelined bus system

The Euclidean distance transform ( EDT) is an operation to convert a binary image consisting of black and white pixels to a representation where each pixel has the Euclidean distance of the nearest black pixel. The EDT has many applications in computer vision and image processing. We present two algorithms for computing the EDT on the linear array with a reconfigurable pipelined bus system (LARPBS), a recently proposed architecture based on optical buses. Our first algorithm runs in O( log log N) time for a binary N× N image on an LARPBS with N 2+ ε processors, for any fixed ε, 0< ε<1. Our second algorithm is highly scalable and runs in O( N 2 p 2 log log p) time if the LARPBS has only p 2+ ε processors for p< N. The previous best deterministic algorithm for computing the EDT on the LARPBS is by Pan et al. Proceedings of IPDPS 2000 Workshop on Parallel and Distributed Computing in Image Processing, Video Processing and Multimedia (PDIVM 2000), Lecture Notes in Computer Science, Vol. 1800, Springer, Berlin, 178). Their algorithm runs either in O( log N log log N) time on an LARPBS with N 2 processors or in O( log log N) time on an LARPBS with O( N 3) processors.

Fault tolerant algorithms for a linear array with a reconfigurable pipelined bus system*

Recently, researchers have proposed many models using reconfigurable optically pipelined buses. All algorithms developed for these models assume that a healthy system is available. We present some fundamental algorithms that are able to tolerate up to N/2 faults on an N-processor, linear array with a reconfigurable pipelined bus system (LARPBS) (one particular optical model). We then extend these results to apply to other algorithms in the areas of image processing and matrix operations.

More Efficient Topological Sort Using Reconfigurable Optical Buses

Topological sort of an acyclic graph has many applications such as job scheduling and network analysis. Due to its importance, it has been tackled on many models. Dekel et al. l3r, proposed an algorithm for solving the problem in O(log2 N) time on the hypercube or shuffle-exchange networks with O(N3) processors. Chaudhuri l2r, gave an O(log N) algorithm using O(N3) processors on a CRCW PRAM model. On the LARPBS (Linear Arrays with a Reconfigurable Pipelined Bus System) model, Li et al. l5r showed that the problem for a weighted directed graph with N vertices can be solved in O(log N) time by using N3 processors. In this paper, a more efficient topological sort algorithm is proposed on the same LARPBS model. We show that the problem can be solved in O(log N) time by using N3/log N processors. We show that the algorithm has better time and processor complexities than the best algorithm on the hypercube, and has the same time complexity but better processor complexity than the best algorithm on the CRCW PRAM model.