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Scalable Parallel Matrix Multiplication on Distributed Memory Parallel Computers
 Journal of Parallel and Distributed Computing
, 2001
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Efficient Parallel Algorithms for Distance Maps of 2D Binary Images Using an Optical Bus
 Model of LPB and LARPBS [11] Segment Switches on an LARPBS [11] 5. Model of LARPBS with Switch Connections [12] 6. Model of LAROB [1] Model of AROB [6] (a) TwoDimensional Reconfigurable Network (b) Switch Configurations 8. Model of
, 2002
"... Computing a distance map (distance transform) is an operation that converts a twodimensional (2D) image consisting of black and white pixels to an image where each pixel has a value or a pair of coordinates that represents the distance to or location of the nearest black pixel. It is a basic opera ..."
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Cited by 5 (3 self)
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Computing a distance map (distance transform) is an operation that converts a twodimensional (2D) image consisting of black and white pixels to an image where each pixel has a value or a pair of coordinates that represents the distance to or location of the nearest black pixel. It is a basic operation in image processing and computer vision fields, and is used for expanding, shrinking, thinning, segmentation, clustering, computing shape, object reconstruction, etc. This paper examines the possibility of implementing the problem of finding a distance map for an image efficiently using an optical bus. The computational model considered is the linear array with a reconfigurable pipelined bus system (LARPBS), which has been introduced recently based on current electronic and optical technologies. It is shown that the problem for an image can be implemented in (log log log ) bus cycles deterministically or in (log ) bus cycles with high probability on an LARPBS with processors. By high probability, we mean a probability of (1 ) for any constant 1. We also show that the problem can be solved in (log log ) bus cycles deterministically or in (1) bus cycles with high probability on an LARPBS with 3 processors. Scalability of the algorithms is also discussed briefly. The same problem can be solved using an LARPBS of processors in (( ) log log log ) time deterministically or in (( ) log ) time with high probability for any practical machine size of . For processor arrays with practical sizes, a bus cycle is roughly the time of an arithmetic operation. Hence, the algorithm compares favorably to the best known parallel algorithms for the same problem in the literature.
Sublogarithmic Deterministic Selection on Arrays with a Reconfigurable Optical Bus
 IEEE Trans. on Computers
, 2002
"... The Linear Array with a Reconfigurable Pipelined Bus System (LARPBS) is a newly introduced parallel computational model, where processors are connected by a reconfigurable optical bus. In this paper, we show that the selection problem can be solved on the LARPBS model deterministically in O((]og l ..."
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Cited by 4 (0 self)
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The Linear Array with a Reconfigurable Pipelined Bus System (LARPBS) is a newly introduced parallel computational model, where processors are connected by a reconfigurable optical bus. In this paper, we show that the selection problem can be solved on the LARPBS model deterministically in O((]og log N)2/]o ]o ]o N) time. To our best knowledge, this is the best deterministic selection algorithm on any model with a reconfigurable optical bus.
Fast and Scalable Parallel Algorithms for Matrix Chain Product and Matrix Powers On Optical Buses
 IN HIGH PERFORMANCE COMPUTING SYSTEMS AND APPLICATIONS
, 1999
"... Given N matrices A 1 , A 2 , ..., AN of size N \Theta N , the matrix chain product problem is to compute A 1 \Theta A 2 \Theta \Delta \Delta \Delta \Theta AN . Given an N \Theta N matrix A, the matrix powers problem is to calculate the first N powers of A, i.e., A, A 2 , A 3 , ..., A N . We s ..."
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Cited by 4 (3 self)
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Given N matrices A 1 , A 2 , ..., AN of size N \Theta N , the matrix chain product problem is to compute A 1 \Theta A 2 \Theta \Delta \Delta \Delta \Theta AN . Given an N \Theta N matrix A, the matrix powers problem is to calculate the first N powers of A, i.e., A, A 2 , A 3 , ..., A N . We show that the two problems can be solved in O ` N ff+1 p + N 2(1+1=ff) p 2=ff log p N + (log N) 2 ' and O ` N ff+1 p + N 2(1+1=ff) p 2=ff log p + log N log p ' times, respectively, where ff ! 2:3755, and p can be arbitrarily chosen in the interval [1::N ff+1 ]. Our algorithms can be implemented on a linear array with a reconfigurable pipelined bus system, which is a distributed memory system using optical interconnections.
Scalable and Efficient Parallel Algorithms for Euclidean Distance Transform on the LARPBS Model
 IEEE Transactions on Parallel and Distributed Systems
, 2004
"... Abstract—A parallel algorithm for Euclidean Distance Transform (EDT) on linear array with reconfigurable pipeline bus system n log n (LARPBS) is presented. For an image with n n pixels, the algorithm can complete EDT transform in O cðnÞ log dðnÞ time using n dðnÞ cðnÞ processors, where cðnÞ and dðnÞ ..."
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Abstract—A parallel algorithm for Euclidean Distance Transform (EDT) on linear array with reconfigurable pipeline bus system n log n (LARPBS) is presented. For an image with n n pixels, the algorithm can complete EDT transform in O cðnÞ log dðnÞ time using n dðnÞ cðnÞ processors, where cðnÞ and dðnÞ are parameters satisfying 1 cðnÞ n, and 1 <dðnÞ n, respectively. By selecting different cðnÞ and dðnÞ, the time complexity and the number of processors used can be adjusted. This makes the algorithm highly scalable and flexible. The algorithm also provides a general framework for EDT algorithms on LARPBS, and many existing and unknown parallel EDT algorithms can be deduced from this framework. In particular, if we let cðnÞ n; dðnÞ n " , the algorithm can be completed in Oð1Þ time using n2þ " processors. To the best of our knowledge, this is the most efficient constanttime EDT algorithm on LARPBS. Index Terms—Distance transform, parallel algorithm, image processing.
Fast and Scalable Parallel Matrix Computations with Optical Buses
, 2000
"... 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 Nth power, the inverse, the characteristic polynomial, the determinant, the ran ..."
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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 Nth power, the inverse, the characteristic polynomial, the determinant, the rank, and an LU and a QRfactorization of a matrix, 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.
Solving Graph Theory Problems Using Recon gurable Pipelined Optical Buses
"... Abstract. We solve a number of important and interesting problems from graph theory on a linear array with a recon gurable pipelined optical bus system. Our algorithms are based on fast matrix multiplication and extreme value nding algorithms, and are currently the fastest algorithms. We also distin ..."
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Abstract. We solve a number of important and interesting problems from graph theory on a linear array with a recon gurable pipelined optical bus system. Our algorithms are based on fast matrix multiplication and extreme value nding algorithms, and are currently the fastest algorithms. We also distinguish the two cases where weights have bounded/unbounded magnitude and precision. 1
Stream PRAM
"... Parallel random access memory, or PRAM, is a now venerable model of parallel computation that that still retains its usefulness for the design and analysis of parallel algorithms. Parallel computational models proposed after PRAM address short comings of PRAM in terms of modeling realism of actual m ..."
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Parallel random access memory, or PRAM, is a now venerable model of parallel computation that that still retains its usefulness for the design and analysis of parallel algorithms. Parallel computational models proposed after PRAM address short comings of PRAM in terms of modeling realism of actual machines. In this work, we propose a multiple instruction stream partitioned PRAM, or "stream PRAM." This model embodies the reality of a small number of parallel processors, each with local memory (which could also be small), where a problem is generally evenly distributed among all processing elements. Actual hardware configurations limit the number of shared memories which can be efficiently implemented. By allowing each shared memory to also act as an independent instruction stream, more functionality is possible with a small extra cost. The additional instruction streams provide limited asynchronous abilities and offer the flexibility of a reconfigurable network as well as allowing the processing elements to perform independent actions. Because the proposed stream PRAM allows variable sizes for processors, memory, and problem sizes, it is valuable for present as well as future parallelism.