S.G. Akl. Parallel Computation Models and Methods. Prentice Hall, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....C 12 C 5 C 6 C 7 C 8 ################ ########### ## ####### ### ##The FFT is an O(n ln n) run time implementation of DFT based on a recursive algorithm proposed by Cooley Tukey. This algorithm can be implemented in dataflow hardware as presented in classical text books on algorithms [10,6,1]. The number of data points is a power of 2. The network of nodes is a butterfly circuit. Each node implements a complex number multipliesaccumulate operation on its inputs: b j = u j z v j . The two 8 array architecture that we use for computing F 8 is based on these circuits and its ....

S. G. Akl. Parallel Computation: Models and Methods. Prentice-Hall, 1997.

....3. 3 Model of Computations The parallel algorithm described later in this paper runs in any model of parallel computations with broadcast bus, where cost of broadcast multicast operation is constant. Among such models are PRAM with a broadcast bus, BSR (Broadcasting with Selective Reduction) [1], LARPBS [22] etc. However, the most adequate for our purposes is simple associative processor model with easy to implement broadcast multicast operations. The model (see Fig.1) consists of single memory cell S and associative memory block A of size n, with memory cells linearly ordered, and ....

....need a single source processor (cell S) to sent identical data to a subset of destination processors (cells) in the blockA. This kind of communication operation is called single node broadcast (multicast, one to subset broadcast) and together with single node accumulation operation n . A[1] A[n] A converter data bus address range A O U T P U T Fig. 1. Model of associative computations. is used in several important parallel algorithms including matrix vector multiplication, vector inner product, Gaussian elimination, and shortest path [15] All processors of ....

Akl, S.G.: Parallel computation: models and methods. Prentice Hall (1997) 475--509

.... coordinates . Step 3: The counts determined in Step 2 are routed back to the originating processors for the individual points. Steps 1 is done in ##### # # time using the OTIS Mesh sort algorithm of [15] Step 2 is an example of the general prefix computation (GPC) operation described in [1]. We shall show below, how to do Step 2 in ### # ### time. Step 3 may be done in ### # # time by sorting on the originating processor indexes. Step 2 can be done in ### # # # time using a divide andconquer algorithm. Let ### ####### ##### # be the sorted point sequence. # be the ....

..... respectively, denote the left and right halves ) denote the point sequence ( reordered by coordinate and within coordinate by coordinate. For each ) let # ) be the point with highest index of # . The the following equations are easily verified [1]: # # ##### # # # # ### # where # # # # is one more than the number of points to the left of # in . We may compute and # in ##### # time on an dimensional mesh by partitioning the mesh into # # processor submeshes, recursively ....

S. Akl. Parallel Computation: Models and Methods. Prentice Hall, 1997.

....the cost of transitive closure. The model does capture how hard it is to gather the information needed to sort. Also, lower bounds in our model will apply to models that take these factors into account. For more realistic models of parallelism see any current textbook on parallel algorithms, e.g. [1, 15]. The rst round of a p processor algorithm takes x # ; x # about which nothing is known and makes p comparisons. This can be represented as an undirected graph G on n vertices with p edges. Hence the search for parallel sorting algorithms will involve nding graphs G that have nice ....

S. Akl. Parallel computation: models and methods. Prentice Hall, 1997.

....2 n) 2 ) comparisons in O( log 2 n) 2 ) stages. This is nonoptimal [1] identifies a sorting network with only O(n log 2 n) comparisons but a very large constant factor. However, bitonic sort continues to be faster than theoretically optimal solutions for all practical problem sizes. In [3, 2] Akl provides a review of the history of parallel sorting and classifies the bitonic sort as being one of many compare and exchange (CAE) based sorts. Such sorts can be efficiently implemented on many different parallel architectures, whose commonality is the CAE component as a fundamental ....

S.G. Akl. Parallel Computation Models and Methods. Prentice Hall, 1997.

....In the following subsections, we focus on three classes of computational models PRAM models, network models, and bridging models since these models have attracted considerable attention from the research community. For an examination of models not discussed here, we refer the reader to [Akl97], LMR95] and [MMT95] 7 P P 0 1 . SHARED MEMORY P p 1 Figure 2.1: The PRAM model. 2.1.1 PRAM The Parallel Random Access Machine (PRAM) FW78] is the most widely used parallel computational model. The PRAM model consists of p sequential processors sharing a global memory as shown in ....

Selim Akl. Parallel Computation: Models and Methods. Prentice Hall, 1997.

....functions as parameters of arrange skeleton. Some legal arrangements which will be used in the rest of the paper are shown in Table 3.3, where a and b are vectors of length n, c is a vector of pairs of length n and s is a scalar. a,b) builds a vector of pairs as described before and proj [1] returns the first element of a particular pair: arrangement description possible result c = a,b) creates tuples (pairs) c[i] a[i] b[i] c :arr[n] 2] s = proj [1] c; projects tuples arrays s = a[1] b[1] s :arr[2] Table 1. Some legal arrangement patterns. a and b are vectors of ....

....of length n, c is a vector of pairs of length n and s is a scalar. a,b) builds a vector of pairs as described before and proj [1] returns the first element of a particular pair: arrangement description possible result c = a,b) creates tuples (pairs) c[i] a[i] b[i] c :arr[n] 2] s = proj [1] c; projects tuples arrays s = a[1] b[1] s :arr[2] Table 1. Some legal arrangement patterns. a and b are vectors of length n. The simplest computational skeleton, map, applies a function, f , to all the elements of an array, arranging results in an array with the same shape, for instance, if ....

[Article contains additional citation context not shown here]

S. G. Akl. Parallel Computation: models and methods. Prentice-Hall, 1997.

....2 n) 2 ) comparisons in O( log 2 n) 2 ) stages. This is nonoptimal [1] identifies a sorting network with only O(n log 2 n) comparisons but a very large constant factor. However, bitonic sort continues to be faster than theoretically optimal solutions for all practical problem sizes. In [3, 2] Akl provides a review of the history of parallel sorting and classifies the bitonic sort as being one of many compare and exchange (CAE) based sorts. Such sorts can be efficiently implemented on many different parallel architectures, whose commonality is the CAE component as a fundamental ....

S.G. Akl. Parallel Computation Models and Methods. Prentice Hall, 1997.

....the cost of transitive closure. The model does capture how hard it is to gather the information needed to sort. Also, lower bounds in our model will apply to models that take these factors into account. For more realistic models of parallelism see any current textbook on parallel algorithms, e.g. [1, 15]. The rst round of a p processor algorithm takes x 1 ; x n about which nothing is known and makes p comparisons. This can be represented as an undirected graph G on n vertices with p edges. Hence the search for parallel sorting algorithms will involve nding graphs G that have nice ....

S. Akl. Parallel computation: models and methods. Prentice Hall, 1997.

....between any two processing elements requires a constant time. The corresponding hardware model is that of a multicomputer, or more specifically, of a network of workstations (now) communicating over a Local Area Network (lan) 13 14 This is to be contrasted with a fixed interconnection network [2], in which communication channels connect individual processing elements in a specific network topology (e.g. a hypercube, butterfly, mesh, etc. This is also to be contrasted with the Parallel Random Access Model [2] in which processing elements communicate using shared memory. Most Exclusive ....

....(lan) 13 14 This is to be contrasted with a fixed interconnection network [2] in which communication channels connect individual processing elements in a specific network topology (e.g. a hypercube, butterfly, mesh, etc. This is also to be contrasted with the Parallel Random Access Model [2], in which processing elements communicate using shared memory. Most Exclusive Read Exclusive Write (erew) pram algorithms map easily to message passing algorithms where each memory read or write becomes a message received or sent. The now model is a loosely coupled parallel model, in which ....

[Article contains additional citation context not shown here]

S. G. Akl. Parallel Computations: Models and Methods. Prentice Hall, 1997.

....and connections of milestones requires no interprocessor communication. However, some interprocessor communication is needed to compute the connected components of the resulting roadmap. The latter problem is well studied in the parallel processing literature and a discussion can be found in [1]. We simply note here that the computation of the roadmap components is far less expensive than the computation of the connections among the milestones and cannot significantly affect the overall scaling of our approach. As far as message passing architectures are concerned, several schemes are ....

S. Akl. Parallel Computation: Models and Methods, Prentice Hall, Englewood Cliffs, NJ, 1997.

No context found.

S.G. Akl, Parallel Computation: Models And Methods, Prentice Hall, Upper Saddle River, New Jersey, 1997.

....a behavior on particular shapes of the search space [9] Later, additional examples of such algorithms were found [3] this time manifesting superunitary behavior in all instances of the solved problem. These algorithms use unconventional, yet realistic paradigms. This direction is continued in [2]. Finally, another approach led to a new paradigm where superunitary behavior is manifested, namely the data accumulating paradigm. In the data accumulating paradigm, introduced in [11] the input is considered as a virtually endless stream. An algorithm pertaining to this paradigm, called a ....

.... is possible for the static case through parallelism, then neither does parallelism help in the data accumulating case) Throughout the paper we use the Random Access Machine (RAM) and the Parallel Random Access Machine (PRAM) as our sequential and parallel computational models respectively [2], unless otherwise stated. 2 The Data Accumulating Paradigm We present here the necessary preliminaries concerning the data accumulating paradigm, conforming to [12] also summarizing the notations used through the paper. A standard algorithm, working on a non varying set of data, is referred to ....

[Article contains additional citation context not shown here]

S. G. Akl, Parallel Computation: Models and Methods, Prentice-Hall, 1997.

....high cost of inverting a computation, and so on. The common property of such situations is the existence of a threshold value for the number of processors. Once the number of processors is smaller than this threshold, more work is required 1 to solve the problem. This direction was continued in [2], where new paradigms are investigated, such as (i) memory lling computations, in which each iteration of the algorithm produces a value and an address where that value is to be stored, and the value produced by an iteration depends on the previously computed values and addresses, or (ii) dealing ....

....the results obtained. We conclude in the last section. In the following, a proposition is a result proved elsewhere. Where possible, the name of the original theorem is provided. Throughout the paper we use the RAM and the PRAM as our sequential and parallel computational models, respectively [2]. 2 Classical Speedup Bounds The most common measure of the performance of a sequential algorithm is the speedup. Given some problem , the speedup of an algorithm that uses p 1 processors over an algorithm that uses p 2 processors with respect to problem is the ratio S(p 2 ; p 1 ) T (p 2 ....

[Article contains additional citation context not shown here]

S. G. Akl, Parallel Computation: Models and Methods, Prentice-Hall, 1997.

....graph. Because of its widespread applicability, developing an efficient parallel tree contraction algorithm was very important. Miller and Reif [19] describe a deterministic algorithm which runs in O(log N) time with O(N) Exclusive Read Exclusive Write Parallel Random Access Machine (EREW PRAM) [2] processors. A single step of their algorithm uses two basic operations to reduce the current binary tree. The RAKE operation removes in parallel all leaves, while the COMPRESS operation is responsible for compressing maximal chains of nodes with only one child. These chains may appear as a ....

....connections are , Gamma and min. As a consequence, we are able to process a binary tree with O(n) nodes in a bottom up fashion, in order to compute the vector associated with the root of the binary tree, in O(log n) time. The model of parallel computation employed in all cases is an EREW PRAM [2]. Some of the algorithms use O(n) such processors in order to complete the task, while others use only O(n= log n) processors, thus achieving cost optimality. However, the important feature of these algorithms is their running time. Such a parallel algorithm will be able to reduce the binary tree ....

S.G. Akl, "Parallel Computation: Models and Methods", Prentice-Hall, Upper Saddle River, New Jersey, 1997.

....(CW,CR) models are more powerful than the exclusive ones, EW,ER) It is also shown in this paper that the RotateSort algorithm for n 2 values a i;j , 0 a i;j n Gamma 1 takes O(1) steps on the n Theta n AROB. The more general case of sorting n general values has been considered in [2, 12, 17, 24]. Of particular interest for us is the possibility of using integer sorting in order to implement efficient algorithms for different packet routing problems. The routing problem requires each processor in a network, which initially stores one packet, to send it to its destination processor without ....

Akl, S. G. Parallel Computation : Models and Methods, Prentice Hall, 1997.

No context found.

S.G. Akl. Parallel Computation Models and Methods. Prentice Hall, 1997.

No context found.

Selim G. Akl. Parallel computation: models and methods. Prentice Hall, 1997.

No context found.

S.G. Akl, Parallel Computation: Models and Methods, Prentice Hall, 1997.

No context found.

S.G. Akl, Parallel Computation: Models and Methods, Prentice Hall, 1997.

No context found.

S. G. Akl, Parallel Computation: Models and Methods, Prentice-Hall, 1997.

No context found.

Akl, S.G.: Parallel computation: models and methods. Prentice Hall (1997) 475--509

No context found.

Akl, S.G., Parallel Computation: Models and Methods, Prentice-Hall, 1997.

No context found.

S. Akl. Parallel Computation: Models and Methods, Prentice Hall, Englewood Cliffs, NJ, 1997.

No context found.

Akl, Selim G. "Parallel Computation Models and Methods". New Jersey: Prentice Hall PTR, 1997.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC