Book ChapterDOI
An On-Line Parallel Algorithm for Node Ranking of Trees
Chia-Wei Lee,Justie Su-Tzu Juan,Tai-Lung Wu +2 more
- pp 384-395
TLDR
A parallel algorithm to find an on-line node ranking for general tree with using O (n 3 / log2 n ) processors on CREW PRAM model is presented.Abstract:
A node ranking of a graph G = (V , E ) is a proper node coloring C : V ****** such that any path in G with end nodes x , y fulfilling C (x ) = C (y ) contains an internal node z with C (z ) > C (x ). In the on-line version of the node ranking problem, the nodes v 1 , v 2 ,..., v n are coming one by one in an arbitrary order; and only the edges of the induced subgraph G [{v 1 , v 2 ,..., v i }] are known when the color for the node v i be chosen. And the assigned color can not be changed later. In this paper, we present a parallel algorithm to find an on-line node ranking for general tree. Our parallel algorithm needs O (n log2 n ) time with using O (n 3 / log2 n ) processors on CREW PRAM model.read more
Citations
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Vertex ranking of asteroidal triple-free graphs
A.J.J. Kloks,H. Müller,C.K. Wong +2 more
TL;DR: In this article, an efficient algorithm for computing the vertex ranking number of an asteroidal triple-free graph is presented, whose running time is bounded by a polynomial in the number of vertices and number of minimal separators of the input graph.
Journal ArticleDOI
On-Line Vertex Ranking of Trees
TL;DR: The on-line ranking number of a graph, also known as tree-depth, is given in terms of maximum degree, diameter, and number of internal vertices and is given as the minimum over all algorithms of the largest label that algorithm can be forced to use.
Competitive versions of vertex ranking and game acquisition, and a problem on proper colorings
TL;DR: In this paper, the authors studied the problem of vertex ranking, a type of node-labeling scheme that models a parallel processing problem, and gave bounds on the list ranking number of trees in terms of maximum degree, diameter, and number of internal vertices.
References
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Book
Introduction to Graph Theory
TL;DR: In this article, the authors introduce the concept of graph coloring and propose a graph coloring algorithm based on the Eulers formula for k-chromatic graphs, which can be seen as a special case of the graph coloring problem.
Book
An introduction to parallel algorithms
TL;DR: This book provides an introduction to the design and analysis of parallel algorithms, with the emphasis on the application of the PRAM model of parallel computation, with all its variants, to algorithm analysis.
Journal ArticleDOI
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
Iain S. Duff,John Reid +1 more
TL;DR: On etend la methode frontale pour resoudre des systemes lineaires d'equations en permettant a plus d'un front d'apparaitre en meme temps.
Journal ArticleDOI
The role of elimination trees in sparse factorization
TL;DR: The role of elimination trees in the direct solution of large sparse linear systems is examined and its relation to sparse Cholesky factorization is discussed.
Book
A textbook of graph theory
R. Balakrishnan,K. Ranganathan +1 more
TL;DR: In this article, direct-directed graphs are used to describe the properties of trees, independent sets and matchings, and Eulerian and Hamiltonian graphs for graph colouring.