Parallel computation of perfect elimination schemes using partition techniques on triangulated graphs

AbstractPerfect elimination schemes (p.e.s.) occur in a number of important problems such as perfect Gaussian elimination. The main objective of this paper is to study the parallel computation of p.e.s. of a triangulated or perfect elimination graph G = (V, E), with n = |V| vertices. We start with the notion of partitioning a triangulated graph into a set of (mutually disjoint) adjacency-level sets and we present a parallel algorithm, based mainly on the properties of the adjacency-level sets, which computes a p.e.s. in time O(log L · log H) using L · H · n2 processors on a CRCW-PRAM. The computation of the adjacency-level sets of a triangulated graph can be done in time O(log L) with L · H · n2 processors within the same type of computational model. Here, L < n and H < n are the length and the height of the graph, respectively

Parallel Computation of Perfect Elimination Schemes Using Partition Techniques on Triangulated Graphs

Perfect elimination schemes (p.e.s.) occur in a number of important problems such as perfect Gaussian elimination. The main objective of this paper is to study the parallel computation of p.e.s, of a triangulated or perfect elimination graph G = (V, E), with n = /V/ vertices. We start with the notion of partitioning a triangulated graph into a set of (mutually disjoint) adjacency-level sets and we present a parallel algorithm, based mainly on the properties of the adjacency-level sets, which computes a p.e.s. in time O(log L . log H) using L . H . n(2) processors on a CRCW-PRAM. The computation of the adjacency-level sets of a triangulated graph can be done in time O(log L) with L . H . n(2) processors within the same type of computational model. Here, L < n and H < n are the length and the height of the graph, respectively.Computers & Mathematics with Application

On the forgotten theorem of Mr. Vincent

SummariesA little known theorem concerning the isolation of roots of polynomial equations, published in 1836 by a mathematician known only as Mr. Vincent, is discussed. Mr. Vincent's method is of historical and practical interest because it requires fewer computations than Sturm's method. The advantages afforded by this theorem are particularly relevant to software systems for computerized algebra. Certain computational results which offer an empirical comparison of the two methods are also presented

Odd-Even, Compare-Exchange Parallel Sorting

We present a parallel sorting algorithm and its proof which sorts a sequence of n elements in time O(log2 n) with n/2 processors on an EREW-PRAM computational model. A sorting network directly implements the algorithm using O(n.log n)PEs. The algorithm is based on the elementary Compare-Exchange operation and has the advantage that it does not require a powerful computational model, uses the least amount of space for the sorting problem, has small constants and can be implemented directly on a sorting network. Furthermore, the architecture of the network is simple and makes no unrealistic technological assumptions.Microprocessing and Microprogrammin

FAST PARALLEL ALGORITHMS FOR FINDING CUTPOINTS AND BRIDGES OF UNDIRECTED GRAPHS

ABSTRACT In this paper we present fast parallel algorithms for finding the cutpoints and bridges of an undirected graph G = (V,E) having n vertices. We start with the notion of partitioning a graph in a set of (mutually disjoint) adjacency-level sets, and we propose a parallel algorithm which computes these sets in time O(logL) using L · H · n2 processors on a CRCW-PRAM, where L < n and H < n. Based on the properties of the adjacency-level sets, we formulate parallel algorithms which locate all cutpoints and bridges of an undirected graph in constant time O(1) by using no more than L · H · n2 processors on a CRCW-PRAM computational model.Parallel Algorithms and Application

On the Parallel Evaluation of Dwba Integrals

The parallel evaluation of Distorted-Wave-Born-Approximation (DWBA) integrals is dis- cussed. A model of computation is presented and used for the description and analysis of parallel algorithms. The computational complexity of DWBA integrals is obtained under unbounded and bounded parallelism. Comparisons with sequential computation are made.International Journal of Computer Mathematic