Abstract
We present a very simple algorithm for the Level Ancestor Problem. A Level Ancestor Query LA(v, d) requests the depth d ancestor of node v. The Level Ancestor Problem is thus: preprocess a given rooted tree T to answer level ancestor queries. While optimal solutions to this problem already exist, our new optimal solution is simple enough to be taught and implemented.
Partially supported by NSF CCR 9820879.
In fact, 22 28
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References
S. Alstrup and J. Holm. Improved algorithms for finding level-ancestors in dynamic trees. In 27th International Colloquium on Automata, Languages and Programming (ICALP’ 00), LNCS. 1853, pages 73–84, 2000.
M. A. Bender, E. Demaine, and M. Farach-Colton. Cache-oblivious B-trees. In 41st Annual Symposium on Foundations of Computer Science (FOCS), pages 399–409, 2000.
M. A. Bender and M. Farach-Colton. The LCA problem revisited. In LATIN, pages 88–94, 2000.
O. Berkman and U. Vishkin. Recursive *-tree parallel data-structure. In Proc. of the 30th IEEE Annual Symp. on Foundation of Computer Science, pages 196–202, 1989.
O. Berkman and U. Vishkin. Recursive star-tree parallel data structure. SIAM J. Comput., 22(2):221–242, Apr. 1993.
O. Berkman and U. Vishkin. Finding level-ancestors in trees. J. Comput. Syst. Sci., 48(2):214–230, Apr. 1994.
R. Cole and R. Hariharan. Dynamic LCA queries on trees. In Proc. of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 235–244, 1999.
P. F. Dietz. Finding level-ancestors in dynamic trees. In Workshop on Algorithms and Data Structures, pages 32–40, 1991.
H. N. Gabow, J. L. Bentley, and R. E. Tarjan. Scaling and related techniques for geometry problems. In Proc. of the 16th Ann. ACM Symp. on Theory of Computing, pages 135–143, 1984.
D. Harel and R. E. Tarjan. Fast algorithms for finding nearest common ancestors. SIAM J. Comput., 13(2):338–355, 1984.
B. Schieber and U. Vishkin. On finding lowest common ancestors: Simplification and parallelization. SIAM J. Comput., 17:1253–1262, 1988.
R. E. Tarjan. Applications of path compression on balanced trees. Journal of the ACM, 26(4):690–715, Oct. 1979.
B. Wang, J. Tsai, and Y. Chuang. The lowest common ancestor problem on a tree with unfixed root. Information Sciences, 119:125–130, 1999.
Z. Wen. New algorithms for the LCA problem and the binary tree reconstruction problem. Inf. Process. Lett., 51(1):11–16, 1994.
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Bender, M.A., Farach-Colton, M. (2002). The Level Ancestor Problem Simplified. In: Rajsbaum, S. (eds) LATIN 2002: Theoretical Informatics. LATIN 2002. Lecture Notes in Computer Science, vol 2286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45995-2_44
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DOI: https://doi.org/10.1007/3-540-45995-2_44
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