This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Recognizing Unordered Depth-First Search Trees of an Undirected Graph in Parallel
June 2000 (vol. 11 no. 6)
pp. 559-570
ASCII Text
x 
 
Chen-Hsing Peng, Biing-Feng Wang, Jia-Shung Wang, "Recognizing Unordered Depth-First Search Trees of an Undirected Graph in Parallel," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 6, pp. 559-570, June, 2000.
 
 
BibTex
x
 
@article{ 10.1109/71.862207,
author = {Chen-Hsing Peng and Biing-Feng Wang and Jia-Shung Wang},
title = {Recognizing Unordered Depth-First Search Trees of an Undirected Graph in Parallel},
journal ={IEEE Transactions on Parallel and Distributed Systems},
volume = {11},
number = {6},
issn = {1045-9219},
year = {2000},
pages = {559-570},
doi = {http://doi.ieeecomputersociety.org/10.1109/71.862207},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Parallel and Distributed Systems
TI - Recognizing Unordered Depth-First Search Trees of an Undirected Graph in Parallel
IS - 6
SN - 1045-9219
SP559
EP570
EPD - 559-570
A1 - Chen-Hsing Peng,
A1 - Biing-Feng Wang,
A1 - Jia-Shung Wang,
PY - 2000
KW - Depth-first search trees
KW - spanning trees
KW - parallel algorithms
KW - PRAM
KW - the Euler-tour technique.
VL - 11
JA - IEEE Transactions on Parallel and Distributed Systems
ER -
 

Abstract—Let $G$ be an undirected graph and $T$ be a spanning tree of $G$. In this paper, an efficient parallel algorithm is proposed for determining whether $T$ is an unordered depth-first search tree of $G$. The proposed algorithm runs in $O(m/p + \log m)$ time using $p$ processors on the EREW PRAM, where $m$ is the number of edges contained in $G$. It is cost-optimal and achieves linear speedup.

[1] A. Aggarwal, R.J. Anerson, and M.-Y. Kao, "Parallel Depth-First Search in General Directed Graphs," SIAM J. Computing, vol. 19, no. 2, pp. 397-409, 1990.
[2] B. Chazelle, "Computing on a Free Tree Via Complexity-Preserving Mapping," Algorithmica, vol. 3, pp. 337-361, 1987.
[3] C.C.-Y. Chen, S.K. Das, and S.G. Akl, "A Unified Approach to Parallel Depth-First Traversals of General Trees," Information Processing Letters, vol. 38, pp. 49-55, 1991.
[4] R. Cole and U. Vishkin, "Approximate Parallel Scheduling. Part 1: The Basic Technique with Applications to Optimal Parallel List Ranking in Logarithmic Time," SIAM J. Computing, vol. 18, pp. 128-142, 1988.
[5] T. Hagerup, "Planar Depth-First Search in$O(\log n)$Parallel Time," SIAM J. Computing, vol 19, no. 4, pp. 678-704, 1990.
[6] J. J'aJ'a, An Introduction to Parallel Algorithms.New York: Addison-Wesley, 1992.
[7] E. Korach and Z. Ostfeld, "DFS Tree Construction: Algorithms and Characterizations," Proc. 14th Int'l Workshop Graph-Theoretic Concepts in Computer Science (WG-88), 1988.
[8] U. Manber, "Recognizing Breadth-First Search Trees in Linear Time," Information Processing Letters, vol. 34, pp. 167-171, 1990.
[9] C.-H. Peng, J.-S. Wang, and R.C.-T. Lee, "Recognizing Shortest-Path Trees in Linear Time," Information Processing Letters, vol. 57, pp. 78-85, 1994.
[10] J.H. Reif, "Depth-First Search Is Inherently Sequential," Information Processing Letters, vol. 20, pp. 229-234, 1985.
[11] C.A. Schevon and J.S. Vitter, "A Parallel Algorithm for Recognizing Unordered Depth-First Search," Information Processing Letters, vol. 28, pp. 105-110, 1988.
[12] B. Schieber and U. Vishkin, "On Finding Lowest Common Ancestors: Simplification and Parallelization," SIAM J. Computing, vol. 17, pp. 1,253-1,262, 1988.
[13] R.E. Tarjan, "Depth-First Search and Linear Graph Algorithms," SIAM J. Computing, vol. 1, pp. 814-830, 1972.
[14] R.E. Tarjan, "Applications of Path Compression on Balanced Trees," J. ACM, vol. 26, pp. 690-715, 1979.
[15] R.E. Tarjan and U. Vishkin, "An Efficient Parallel Biconnectivity Algorithm," SIAM J. Computing, vol. 14, pp. 862-874, 1985.
[16] U. Vishkin, "On Efficient Parallel Strong Orientation," Information Processing Letters, vol. 20, pp. 235-240, 1988.

Index Terms:
Depth-first search trees, spanning trees, parallel algorithms, PRAM, the Euler-tour technique.
Citation:
Chen-Hsing Peng, Biing-Feng Wang, Jia-Shung Wang, "Recognizing Unordered Depth-First Search Trees of an Undirected Graph in Parallel," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 6, pp. 559-570, June 2000, doi:10.1109/71.862207
Usage of this product signifies your acceptance of the Terms of Use.