Information Processing Letters
Optimal node ranking of trees in linear time
Information Processing Letters
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
On an edge ranking problem of trees and graphs
Discrete Applied Mathematics
An introduction to parallel algorithms
An introduction to parallel algorithms
On a graph partition problem with application to VLSI layout
Information Processing Letters
Discrete Mathematics
Generalized vertex-rankings of trees
Information Processing Letters
Parallel computation: models and methods
Parallel computation: models and methods
An optimal parallel algorithm for node ranking of cographs
Discrete Applied Mathematics
Optimal edge ranking to trees in polynomial time
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Discrete Mathematics
Biconvex graphs: ordering and algorithms
Discrete Applied Mathematics
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Algorithms for generalized vertex-rankings of partial k-trees
Theoretical Computer Science - computing and combinatorics
Vertex Ranking of Asteroidal Triple-Free Graphs
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
On Vertex Ranking for Permutations and Other Graphs
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Approximating Treewidth, Pathwidth, and Minimum Elimination Tree Height
WG '91 Proceedings of the 17th International Workshop
An optimal parallel algorithm for c-vertex-ranking of trees
Information Processing Letters
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
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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.