Joseph Jaja. An Introduction to Parallel Algorithms. AddisonWesley, Reading, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....optical bus, time complexity 1. Introduction Many applications can be represented as an acyclic graph. The topological sort of an acyclic graph is to find a linear ordering for the vertices of the graph, such that if (i, j) is an edge of the graph, then i appears before j in the ordering [4]. If the graph is not acyclic then no linear ordering is possible. A topological sort of a directed graph can be viewed as an ordering of its vertices along a horizontal line, so that all directed edges go from left to right. Topological sort has many applications in various job scheduling, ....

....then no linear ordering is possible. A topological sort of a directed graph can be viewed as an ordering of its vertices along a horizontal line, so that all directed edges go from left to right. Topological sort has many applications in various job scheduling, network analysis, and other areas [1, 4]. The topological sort problem has been tackled on many models. For example, Dekel et al. proposed an algorithm for solving the problem in O(log 2 N) time on the hypercube or shuffle exchange networks with O(N 3) processors [3] Chaudhuri also gave an O(log N) algorithm using O(N 3) processors on ....

Joseph JfiJfi. An Introduction to Parallel Algorithms. Addison-Wesley Publishing Company, Reading, Massachusetts, 1992.

....updated in ( N) time. There are (log( ffl ) iterations, for a total time of ( N log( ffl ) To implement the algorithm in parallel, implement each iteration in parallel. Each iteration can be implemented using standard techniques in (log N) time with ( N) operations on an EREW PRAM [7]. 4 l o s eran o zat on o eore Obliviously derandomizing Theorem 3 yields a generalization of the greedy set cover algorithm. We briefly sketch the analysis. For the remainder of this section, we assume only that each P ij is non negative. For this theorem, we want to find a multi set S of k ....

Joseph J'aJ'a. Introduction to Parallel Algorithms. Addison-Wesley Publishing Company, Inc., 1992.

....of size m. This eliminates the sending of requested element addresses from the intermediate to source processors, reducing time taken by pr In p. 8 CREW CRCW PRAM Simulation The PRAM is a shared memory parallel programming model that has been widely used for the design of parallel algorithms [13]. It is an abstract model which does not differentiate between the cost of unit computation and unit communication. By simulating a PRAM on a more realistic (but still sufficiently general) model, an efficient and reasonably architecture independent implementation of shared memory on distributed ....

Joseph Jaja. An Introduction to Parallel Algorithms Addison-Wesley, 1992.

....can construct one from the other by replacing all balancers by comparators and vice versa. Theorem 4.8 (Counting vs. Sorting) The isomorphic network of a Counting Network is a Sorting Network but not vice versa. Proof: The isomorphic networks of the Even Odd or Insertion Sorting Network [Knu73, Ja 92, CLR92] are not Counting Networks. For the other direction, let C be a Counting Network and I(C) be the isomorphic network, where every balancer is replaced by a comparator. Let I(C) have an arbitrary input of 0 s and 1 s; that is, some of the input wires have a 0, all others have a 1. There is ....

Joseph Ja'ja'. An Introduction to Parallel Algorithms. Addison -Wesley, Reading, 1992.

....in the Tree of Life (Figure 2) M(z) is also amniote, while y and w both map to jawed vertebrate. An algorithm for constructing the mapping, M, and identifying duplication nodes has been developed in the context of using multiple gene trees to generate a species tree. By using fast lca queries [10] 1 , M can be computed in linear time. While our goals are different, we share a key algorithmic component with this work. We refer the reader to [15] for a complete description and proofs. Observe that under the mapping, a node n in G is a speciation node if its children are mapped to inde ....

Joseph JJ. Introduction to Parallel Algorithms. Addison-Wesley, Reading, MA, 1991.

....communication into adjacent nodes. Bibliographic notes The model described here can remind the reader of several other ones. There are several common points with a systolic data flow model. The notion of a parallel network with global communications and local ones has also been introduced in [9], pp 7 20. Note that this book refers to notions of global read and global write to communicate from the common memory to all the domains at one time. The strategy of communicating globally to all domains at the same time is either efficient or not Intra domain communication (cost Cclose) ....

Joseph J`aj`a. An introduction to parallel algorithms. Addison-Wesley, Reading, Ma., USA, 1992.

....used to solve a given problem jointly. 3.2.1 Parallel Machine Model The RAM (Random Access Machine) is a model used successfully to predict the performance of programs on single processor (sequential) computers. A natural extension of this model for parallel computers is the shared memory model [14]. This model consists of a number of processors, each of which has its own local memory and can execute its own local program, and all of which communicate by exchanging data through a shared memory unit, also called global memory. There are two basic modes of operation of a shared memory model: ....

....three PRAM models (EREW, CREW, CRCW) do not differ substantially in their computational power. Computation made on a p processor, one variant of the PRAM model, can be simulated on another CHAPTER 3. MULTIPROCESSOR PARALLEL PROCESSING 20 variant with a slowdown of a factor no larger than O(log p) [14]. 3.2.2 Parallel Complexity A parallel algorithm is considered efficient if it requires polylogarithmic parallel time ( O(log k n) while the number of processors it uses is polynomial in the size of the input (O(n k ) The class of problems that can be solved by efficient parallel ....

[Article contains additional citation context not shown here]

Joseph J'aj'a. An Introduction to Parallel Algorithms. Addison-Wesley, 1992.

....with small constant factors, and a worst case runtime of O(n 2 ) Besides its good performance in practice, Quicksort sorts in place: it needs only O(log n) storage in addition to that needed for the array A. There are parallelizations of Quicksort, which need (n) additional space (see, e.g. [11]) and therefore are not in place. We count algorithms using (n) processors to this class, since each processor has at least one local variable. In this paper, the in place variant of parallel Quicksort from [9] is investigated. This Quicksort variant uses only O(p log n) extra storage, where p ....

Joseph Jaja. An Introduction to Parallel Algorithms. Addison-Wesley, 1992.

.... node and the cost of computing each value is O(n 2 ) the cost of computing all the M values of any node is O(n 6 ) As there are O(k) nodes in the separating tree the total cost of the algorithm is O(n 6 ) and time complexity is O(d log n) 25 We conjecture that Parallel Tree Contraction [6, 8] technique might be helpful in decreasing the parallel time complexity of both the problems discussed. 26 Chapter 5 Longest Increasing Subsequence The Longest Increasing Subsequence problem is the following: We are given permutation T = t 1 ; t 2 ; t n ) of 1 to n. We wish to know ....

Joseph Ja Ja. An Introduction to Parallel Algorithms. Addison-Wesley, 1992.

....knows about all other nodes in the network, can now broadcast the pointers to the entire network in one time step. Note that in the first procedure of stage 1, each node independently decides to be active or inactive. This is similar to the pointer jumping techniques used in parallel algorithms [2]. The Absorption algorithm assumes a stronglyconnected graph. On a weakly connected graph, we can run the Name Dropper algorithm [1] for O(log n) time steps to obtain a strongly connected graph with high probability. 4 Performance Analysis This section analyzes Absorption s asymptotic ....

Joseph Jaja. An Introduction to Parallel Algorithms. AddisonWesley, Reading, 1992.

....cause a significant slowdown. We are convinced that performance will improve when our Modula 2 compiler implements alignment and exploits locality of reference in the near future. 4 Test Problems and Results At this time, our benchmark suite consists of nine problems collected from literature [1, 4, 8, 5]. For each problem, we implemented the same algorithm in Modula 2 in C, and in MPL 2 . Then we measured the runtimes of our implementations on a 16k MasPar MP 1 and a Sparc 1 for widely ranging problem sizes. In the Modula 2 programs, we use highly efficient library routines such as reductions ....

....4.2 List Rank Problem: A linked list of n elements is given. All elements are stored in an array A[1: n] Compute for each element its rank in the list. Approach: This problem is solved by pointer jumping. Note: Ranking the elements of a list is one of the elementary list processing tasks [8]. 0.25 0.5 0.75 1 2 6 2 8 2 10 2 12 2 14 2 16 2 18 2 20 2 22 problem size Problem ListRank t(c) t(m2 ) t(mpl) t(m2 ) The good result is caused by the fact that both MPL and Modula 2 must use general communication. Again, the general implementation of virtualization loops by the ....

Joseph J'aJ'a. An Introduction to Parallel Algorithms. Addison-Wesley, Reading, Mass., 1992.

....and omitted. Finally k(x) illustrates a more complex divide and conquer recursion, in which the input x is divided either into 2 subproblems or into 3: the translation into map recursion is, again, straightforward and omitted. An informal examination of a variety of parallel algorithms [40, 7] persuaded us that map recursion suffices to express in a natural way large classes of parallel algorithms. It is easy to write a preprocessor which translates recursive schemas like those in figure Figure 7 into map recursive definitions, and in the process parallelizes them. One wonders which ....

....T = O(1) while keeping the work complexity under control. Of course, if we want work optimality first of all, we can obtain W = O(n log n) Proposition 4.3 CoPa can express sort with complexities T = O(log n log log n) and W = O(n log n) Proof. This is achieved with Valiant s merge algorithm [74, 40], which can be expressed in CoPa; note that we need a user defined external sorting function to express the last part of the algorithm (sequential merging of small sequences) 2 Once we have sorting, set and bag operations can be implemented straightforwardly as sorted sequences. The only catch ....

[Article contains additional citation context not shown here]

Joseph Jaja. An Introduction to Parallel Algorithms. Addison-Wesley, 1992.

....R d . Furthermore, no simplex intersects more than jHj=r hyperplanes. The number of simplices in C is called the size of the cutting. The derandomization methods are actually techniques for constructing cuttings whose existence is guaranteed by the probabilistic method. It was shown by Matousek [25] and Chazelle [7] that 1=r cuttings of size O(r d ) can be constructed in time O(n r d 1 ) using a derandomization technique based on the method of conditional probabilities (known as Raghavan Spencer technique) It is fairly clear that, given such a cutting, the multidimensional search ....

Joseph Ja' Ja'. Introduction to Parallel Algorithms, Addison Wesley. 1992.

No context found.

Joseph Jaja. An Introduction to Parallel Algorithms. AddisonWesley, Reading, 1992.

No context found.

Joseph JaJa: An Introduction to Parallel Algorithms. Addison-Wesley, 1992

No context found.

Joseph Jaja. An Introduction to Parallel Algorithms. Addison-Wesley, Reading, MA, 1992.

No context found.

Joseph J aJ a. 1992. An introduction to Parallel Algorithms. Addison-Wesley.

No context found.

Joseph JaJa. Introduction to Parallel Algorithms. Addison-Wesley, Reading, MA, 1991.

No context found.

Joseph JaJa. An Introduction to Parallel Algorithms. Addison-Wesley Publishing Company, Reading, MA, 1992.

No context found.

Joseph J'aJ'a. An Introduction to Parallel Algorithms. Addison--Wesley Publishing Company, 1992.

No context found.

Joseph Ja Ja, "An Introduction to Parallel Algorithms," Addison Wesley Publishing Company, 1992.

No context found.

Joseph Jaja. An Introduction to Parallel Algorithms. Addison Wesley, 1992.

No context found.

Joseph JaJa. An Introduction to Parallel Algorithms. AddisonWesley Publishing Company, 1992.

No context found.

Joseph JaJa. Introduction to Parallel Algorithms. Addison-Wesley, Reading, MA, 1991.

No context found.

Joseph J'aJ'a. Introduction to Parallel Algorithms. Addison-Wesley Publishing Company, Inc., 1992.

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