Abstract
Depth First Search (DFS) tree is a fundamental data structure for graphs used in solving various algorithmic problems. However, very few results are known for maintaining DFS tree in a dynamic environment - insertion or deletion of edges. The only non-trivial result for this problem is by Franciosa et al. [4]. They showed that, for a directed acyclic graph on n vertices, a DFS tree can be maintained in O(n) amortized time per edge insertion. They stated it as an open problem to maintain a DFS tree dynamically in an undirected graph or general directed graph.
We present the first algorithm for maintaining a DFS tree for an undirected graph under insertion of edges. For processing any arbitrary online sequence of edge insertions, this algorithm takes total O(n 2) time.
Full version of this paper is available at http://www.cse.iitk.ac.in/users/ sbaswana/Papers-published/Incr-DFS.pdf
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alstrup, S., Holm, J.: Improved algorithms for finding level ancestors in dynamic trees. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 73–84. Springer, Heidelberg (2000)
Cole, R., Hariharan, R.: Dynamic lca queries on trees. SIAM J. Comput. 34(4), 894–923 (2005)
Even, S., Shiloach, Y.: An on-line edge-deletion problem. J. ACM 28(1), 1–4 (1981)
Franciosa, P.G., Gambosi, G., Nanni, U.: The incremental maintenance of a depth-first-search tree in directed acyclic graphs. Inf. Process. Lett. 61(2), 113–120 (1997)
Miltersen, P.B., Subramanian, S., Vitter, J.S., Tamassia, R.: Complexity models for incremental computation. Theor. Comput. Sci. 130(1), 203–236 (1994)
Reif, J.H.: Depth-first search is inherently sequential. Inf. Process. Lett. 20(5), 229–234 (1985)
Reif, J.H.: A topological approach to dynamic graph connectivity. Inf. Process. Lett. 25(1), 65–70 (1987)
Roditty, L., Zwick, U.: On dynamic shortest paths problems. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 580–591. Springer, Heidelberg (2004)
Tarjan, R.E.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146–160 (1972)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baswana, S., Khan, S. (2014). Incremental Algorithm for Maintaining DFS Tree for Undirected Graphs. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-662-43948-7_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-43947-0
Online ISBN: 978-3-662-43948-7
eBook Packages: Computer ScienceComputer Science (R0)