Journal ArticleDOI
Efficient parallel algorithms for series parallel graphs
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TLDR
A parallel algorithm for recognizing series parallel graphs and constructing decomposition trees and takes O(log2 n + log m) time with O(n + m) processors, where n (m) is the number of vertices (edges) in the graph.About:
This article is published in Journal of Algorithms.The article was published on 1991-09-01. It has received 30 citations till now. The article focuses on the topics: Spanning tree & Time complexity.read more
Citations
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Journal ArticleDOI
Routing in Series Parallel Networks
TL;DR: The time and space complexities of Distance Routing in Series Parallel Graphs are computed, and they are compared with the relative complexities of Interval Routing, showing the improvement of distance Routing especially in terms of time complexity.
Journal ArticleDOI
Fast Algorithms forK4Immersion Testing
TL;DR: This paper presents for the first time a fast, practical algorithm to determine whether an arbitrary input graph contains K4 in the immersion order, and extends the method so that, should an immersedK4be present, aK4model is isolated.
Dissertation
Bounded combinatorial width and forbidden substructures
TL;DR: In this article, an algebraic enumeration scheme for graphs is proposed to find all minor-order forbidden graphs for each fixed pathwidth, where the main assumption is that an upper bound on the pathwidth (or treewidth) of a particular graph family is more readily available than its order or size.
Proceedings Article
Parallel Decomposition of Generalized Series-Parallel Graphs.
TL;DR: In this article, an efficient parallel algorithm for constructing a decomposition tree of a given generalized series-parallel (GSP) graph is presented, which takes O(log n) time with C(m, n) processors on a CRCW PRAM, where m is the number of processors required to find connected components of a graph with in edges and n vertices in logarithmic time.
Tactical communications network modelling and reliability analysis: An overview
TL;DR: This report summarizes a survey of the literature on network reliability problems that arise in modeling communication networks and includes brief tutorials on the graph-theoretic concepts.
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Book
Graph theory with applications
TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
Journal ArticleDOI
Graph theory with applications (revised edition), by J. A. Bondy and U.S.R. Murty. Pp x, 264. £5·95 paperback. 1977. SBN 0 333 22694 1 (Macmillan)
Proceedings ArticleDOI
Matrix multiplication via arithmetic progressions
Don Coppersmith,Shmuel Winograd +1 more
TL;DR: A new method for accelerating matrix multiplication asymptotically is presented, by using a basic trilinear form which is not a matrix product, and making novel use of the Salem-Spencer Theorem.
Journal ArticleDOI
The Recognition of Series Parallel Digraphs
TL;DR: A linear-time algorithm to recognize the class of vertex series-parallel (VSP) digraphs is presented and efficient methods to compute the transitive closure and transitive reduction of VSPDigraphs are obtained.