Parallel Algorithms for Intersection Graphs


Book Description

Let $\cal F$ be a family of nonempty sets. Then the intersection graph of $\cal F$ is obtained by representing each set in $\cal F$ by a vertex and connecting two vertices if and only if their corresponding sets have a nonempty intersection. In this dissertation, several types of intersection graphs will be examined, among them interval, comparability, chordal, path, and circle graphs. Interval and comparability graphs arise often when solving scheduling problems. Chordal graphs have applications in solving sparse systems of linear equations and in relational database theory.




Sequential and Parallel Algorithms on Intersection Graphs


Book Description

This monogram presents some sequential and parallel algorithms on intersection graphs. The algorithms are designed to solve some problems on interval, permutation and circular arc graphs. These algorithms measure some parameters on intersection graphs.This monogram presents some sequential and parallel algorithms on intersection graphs. The algorithms are deigned to solve some problems on interval, permutation and circular arc graphs. These algorithms measure some parameters on intersection graphs.




Introduction to Parallel Algorithms


Book Description

Parallel algorithms Made Easy The complexity of today's applications coupled with the widespread use of parallel computing has made the design and analysis of parallel algorithms topics of growing interest. This volume fills a need in the field for an introductory treatment of parallel algorithms-appropriate even at the undergraduate level, where no other textbooks on the subject exist. It features a systematic approach to the latest design techniques, providing analysis and implementation details for each parallel algorithm described in the book. Introduction to Parallel Algorithms covers foundations of parallel computing; parallel algorithms for trees and graphs; parallel algorithms for sorting, searching, and merging; and numerical algorithms. This remarkable book: * Presents basic concepts in clear and simple terms * Incorporates numerous examples to enhance students' understanding * Shows how to develop parallel algorithms for all classical problems in computer science, mathematics, and engineering * Employs extensive illustrations of new design techniques * Discusses parallel algorithms in the context of PRAM model * Includes end-of-chapter exercises and detailed references on parallel computing. This book enables universities to offer parallel algorithm courses at the senior undergraduate level in computer science and engineering. It is also an invaluable text/reference for graduate students, scientists, and engineers in computer science, mathematics, and engineering.




Parallel Algorithms for Regular Architectures


Book Description

Parallel-Algorithms for Regular Architectures is the first book to concentrate exclusively on algorithms and paradigms for programming parallel computers such as the hypercube, mesh, pyramid, and mesh-of-trees.




Fast Parallel Algorithms for Graph Matching Problems


Book Description

The matching problem is central to graph theory and the theory of algorithms. This book provides a comprehensive and straightforward introduction to the basic methods for designing efficient parallel algorithms for graph matching problems. Written for students at the beginning graduate level, the exposition is largely self-contained and example-driven; prerequisites have been kept to a minimum by including relevant background material. The book contains full details of several new techniques and will be of interest to researchers in computer science, operations research, discrete mathematics, and electrical engineering. The main theoretical tools are presented in three independent chapters, devoted to combinatorial tools, probabilistic tools, and algebraic tools. One of the goals of the book is to show how these three approaches can be combined to develop efficient parallel algorithms. The book represents a meeting point of interesting algorithmic techniques and opens up new algebraic and geometric areas.




Efficient Parallel Algorithms


Book Description

Mathematics of Computing -- Parallelism.




Efficient Parallel Algorithms on Chordal Graphs with a Sparse Tree Representation


Book Description

Abstract: "Chordal graphs are nothing else than intersection graphs of subtrees of a tree. We present nearly optimal algorithms for certain graph problems if the input graph is given by a collection of subtrees of a tree and the subtrees are given by their leaves. This generalizes results of Olariu, Schwing, and Zhang [12] concerning the parallel complexity of problems on interval graphs provided the interval structure is given."




Topics in Intersection Graph Theory


Book Description

Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics.




Logarithmic Time Parallel Algorithms for Comparability and Interval Graphs


Book Description

We give fast parallel algorithms for recognizing ad representing comparability graphs that can be transitively oriented, and interval graphs, the intersection graphs of intervals along the real line. Under the CRCW PRAM model, both algorithms use $O(n[superscript]{3})$ processors in $O$(log $n$) time to check if a graph belongs to the desired class, and if it does then a valid representation of the graph can be produced. The algorithms gain their efficiency by using fast algorithms for finding the modular decomposition of a graph. Both problems were known to be in $NC$, but the known algorithms require more time than ours does.