Abstract
The Depth First Search (DFS) algorithm is one of the basic techniques which is used in a very large variety of graph algorithms. Every application of the DFS involves, beside traversing the graph, constructing a special structured tree, called a DFS tree. In this paper, we give a complete characterization of all the graphs in which every spanning tree is a DFS tree. These graphs are called Total-DFS-Graphs. The characterization we present shows that a large variety of graphs are not Total-DFS-Graphs, and therefore the following question is naturally raised: Given an undirected graph G=(V,E) and an undirected spanning tree T, is T a DFS tree of G? We give an algorithm to answer this question in linear (O(|E|)) time.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. Aggarwal and R.J. Anderson, A random NC algorithm for depth-first search, In Proc. of the 19th ACM Symposium on Theory of Computation, 325–334, (1987). To appear in Combinatorica.
B. Awerbuch, A new distributed depth-first-search algorithm, Information Processing Letters, 20 (3), 147–150, (1985).
N.L. Biggs, E.K. Lyod and R.J. Wilson, Graph Theory 1736–1936, Clarendon Press, Oxford, (1977).
S. Even, Graph Algorithms, Computer Science Press, Potomac, MD, (1979).
T. Hagerup and M. Nowak, Recognition of Spanning Trees Defined by Graph Searches, Technical Report A 85/08, Universität des Saarlandes, Saarbrücken, West Germany, June 1985.
J.E. Hopcroft and R.E. Tarjan, Dividing a graph into triconnected components, SIAM Journal on Computing, 2(3), (1973).
J.E. Hopcroft and R.E. Tarjan, Efficient algorithms for graph manipulation, Comm. ACM, 16(6), 372–378, (1973).
J.E. Hopcroft and R.E. Tarjan, Efficient planarity testing, J. ACM, 21, 549–568, (1974).
E. Korach and Z. Ostfeld, On the Possibilities of DFS Tree Constructions: Sequential and Parallel Algorithms, Technical Report no. 508, CS Dept. Technion, May 1988.
K.B. Lakshmanan, N. Meenakshi and K. Thulasiraman, A time-optimal message-efficient distributed algorithm for Depth-first-Search, Information Processing Letters, 25, 103–109, (1987).
A. LaPaugh and C.H. Papadimitriou, The even-path problem for graphs and digraphs, Networks, 14, 507–513, (1984).
J.H. Reif, Depth-first search is inherently sequential, Information Processing Letters, 20, 229–234, (1985).
M.M. Syslo, Series-parallel graphs and depth-first search trees, IEEE Transactions on Circuits and Systems, 31(12), 1029–1033, (1984).
R.E. Tarjan and U. Vishkin, An efficient parallel biconnectivity algorithm, SIAM Journal on Computing, 14(4), 862–874, (1985).
R.E. Tarjan, Depth-first search and linear graph algorithms, SIAM Journal on Computing, 1, 146–160, (1972).
P. Tiwari An Efficient Parallel Algorithm for Shifting the Root of a Depth First Spanning Tree, Journal of Algorithms, 7, 105–119, (1986).
W.T. Tutte, Lectures on matroids, J. Res. Nat. Bur. Stand. 69B, 1–48, (1965).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Korach, E., Ostfeld, Z. (1989). DFS tree construction: Algorithms and characterizations. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1988. Lecture Notes in Computer Science, vol 344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50728-0_37
Download citation
DOI: https://doi.org/10.1007/3-540-50728-0_37
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50728-4
Online ISBN: 978-3-540-46076-3
eBook Packages: Springer Book Archive