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.




Parallel Algorithms for Maximum Matching and Other Problems on Interval Graphs


Book Description

In this paper, we consider parallel algorithms on interval graphs. An interval graph is a graph having a one-to-one correspondence with a sequence of intervals on the real line, such that each vertex maps to an interval in the sequence and an edge exists between two vertices if and only if the corresponding intervals overlap. Throughout the paper we use the CREW PRAM model. Our main result is an $O(\log[superscript]{2} n)$ time, $O(n[superscript]{6}/\log n)$ processor algorithm for maximum matching on interval graphs. We give PT-optimal algorithms for maximum weighted clique, maximum independent set, minimum clique cover, and minimum dominating set for representations of interval graphs; and Hamiltonian circuit for representations of proper interval graphs. We also give an improved algorithm for minimum bandwidth on representations of proper interval graphs. In addition, we present $O (\log n)$ time, $O (n[superscript]{2}/\log n)$ processor algorithms for depth-first search on representations of interval graphs and maximum matching on representations of proper interval graphs.




SIAM Journal on Computing


Book Description




Efficient Parallel Algorithms


Book Description

Mathematics of Computing -- Parallelism.




Parallel Computing Technologies


Book Description

This book constitutes the refereed proceedings of the Fourth International Conference on Parallel Computing Technologies, PaCT-97, held in Yaroslavl, Russia, in September 1997. The volume presents a total of 54 contributions: 21 full papers, 20 short papers, 10 posters, and three tutorials. All papers were selected for inclusion in the proceedings from numerous submissions on the basis of three independent reviews. The volume covers all current topics in parallel processing; it is divided into sections on theory, software, hardware and architecture, applications, posters, and tutorials.




Computational Graph Theory


Book Description

One ofthe most important aspects in research fields where mathematics is "applied is the construction of a formal model of a real system. As for structural relations, graphs have turned out to provide the most appropriate tool for setting up the mathematical model. This is certainly one of the reasons for the rapid expansion in graph theory during the last decades. Furthermore, in recent years it also became clear that the two disciplines of graph theory and computer science have very much in common, and that each one has been capable of assisting significantly in the development of the other. On one hand, graph theorists have found that many of their problems can be solved by the use of com puting techniques, and on the other hand, computer scientists have realized that many of their concepts, with which they have to deal, may be conveniently expressed in the lan guage of graph theory, and that standard results in graph theory are often very relevant to the solution of problems concerning them. As a consequence, a tremendous number of publications has appeared, dealing with graphtheoretical problems from a computational point of view or treating computational problems using graph theoretical concepts.




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.







Advances in Computing and Information - ICCI '91


Book Description

This volume contains papers presented at the Third International Conference on Computing and Information, ICCI '91, held at Carleton University in Ottawa, Canada, May 27-29, 1991. The conference was organized by the School of Computer Science at Carleton University, and was sponsored by the Natural Sciences and Engineering Research Council of Canada (NSERC) and Carleton University. ICCI '91 was an international forum for the presentation of original results in research, development, and applications in computing and information processing. The conference was aimed at both practitioners and theoreticians, and was organized into five streams: - Algorithms and complexity, - Databases and information systems, - Parallel processing and systems, - Distributed computing and systems, - Expert systems, artificial intelligence. This volume contains three invited papers, by E.C.R. Hehner, R.L. Probert, and S.J. Smith, and 71 selected papers.