Years and Authors of Summarized Original Work
1984; Gabow, Bentley, Tarjan
1984; Harel, Tarjan
1989; Berkman, Breslauer, Galil, Schieber, Vishkin
2000; Bender, Farach-Colton
Problem Definition
One of the most fundamental algorithmic problems on trees is how to find the lowest common ancestor (LCA) of a pair of nodes. The LCA of nodes u and v in a tree is the shared ancestor of u and v that is located farthest from the root. More formally, the lowest common ancestor (LCA) problem is:
- Preprocess: :
-
A rooted tree T having n nodes.
- Query: :
-
For nodes u and v of tree T, query lca T (u, v) returns the least common ancestor of u and v in T, that is, it returns the node farthest from the root that is an ancestor of both u and v. (When the context is clear, we drop the subscript T on the lca.)
The goal is to optimize both the preprocessing time and the query time. We will therefore refer to the running time of an algorithm with preprocessing time T P (N) and query time of T Q (N) as having run...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Recommended Reading
Alstrup S, Gavoille C, Kaplan H, Rauhe T (2004) Nearest common ancestors: a survey and a new algorithm for a distributed environment. Theory Comput Syst 37(3):441–456
Bender MA, Farach-Colton M (2000) The LCA problem revisited. In: Proceedings of Latin American theoretical informatics (LATIN), Montevideo, pp 88–94
Berkman O, Breslauer D, Galil Z, Schieber B, Vishkin U (1989) Highly parallelizable problems. In: Proceedings of the 21st annual ACM symposium on theory of computing, New Orleans, pp 309–319
Bille P (2014) Nearest common ancestors. http://massivedatasets.files.wordpress.com/2014/02/nearestcommonancestors_2014.pdf
Fischer J (2010) Optimal succinctness for range minimum queries. In: Proceedings of LATIN, Oaxaca, pp 158–169
Gabow HN, Bentley JL, Tarjan RE (1984) Scaling and related techniques for geometry problems. In: Proceedings of the 16th annual ACM symposium on theory of computing, New York, vol 67, pp 135–143
Harel D, Tarjan RE (1984) Fast algorithms for finding nearest common ancestors. SIAM J Comput 13(2):338–355
Navarro G, Sadakane K (2014) Fully functional static and dynamic succinct trees. ACM Trans Algorithms 10(3)
Sadakane K (2002) Space-efficient data structures for flexible text retrieval systems. In: International symposium on algorithms and computation (ISAAC), Vancouver, pp 14–24
Sadakane K (2002) Succinct representations of lcp information and improvements in the compressed suffix arrays. In: Proceedings of the 13th annual ACM-SIAM symposium on discrete algorithms, San Francisco, pp 225–232
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media New York
About this entry
Cite this entry
Farach-Colton, M. (2016). Lowest Common Ancestors in Trees. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_630
Download citation
DOI: https://doi.org/10.1007/978-1-4939-2864-4_630
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2863-7
Online ISBN: 978-1-4939-2864-4
eBook Packages: Computer ScienceReference Module Computer Science and Engineering