Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
A linear algorithm for finding dominators in flow graphs and related problems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
The nearest common ancestor in a dynamic tree
Acta Informatica
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
A data structure for dynamic trees
Journal of Computer and System Sciences
The cell probe complexity of dynamic data structures
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Recognizing breadth-first search trees in linear time
Information Processing Letters
Verification and sensitivity analysis of minimum spanning trees in linear time
SIAM Journal on Computing
Recursive star-tree parallel data structure
SIAM Journal on Computing
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Finding level-ancestors in trees
Journal of Computer and System Sciences
Parallel shortcutting of rooted trees
Journal of Algorithms
Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Optimal bounds for the predecessor problem
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Worst-case and amortised optimality in union-find (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
Optimal Pointer Algorithms for Finding Nearest Common Ancestors in Dynamic Trees
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Maintaining Center and Median in Dynamic Trees
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Minimizing Diameters of Dynamic Trees
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Space-time tradeoff for answering range queries (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
A scaling algorithm for weighted matching on general graphs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Approximate Distance Oracles Revisited
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
The Level Ancestor Problem Simplified
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Path Minima in Incremental Unrooted Trees
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Path minima queries in dynamic weighted trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Succinct representations of permutations and functions
Theoretical Computer Science
Fingerprints in compressed strings
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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Given a node x at depth d in a rooted tree Level Ancestor(x; i) returns the ancestor to x in depth d - i. We show how to maintain a tree under addition of new leaves so that updates and level ancestor queries are being performed in worst case constant time. Given a forest of trees with n nodes where edges can be added, m queries and updates take O(mα(m, n)) time. This solves two open problems (P.F. Dietz, Finding level-ancestors in dynamic trees, LNCS, 519:32-40, 1991). In a tree with node weights, min(x, y) report the node with minimum weight on the path between the nodes x and y. We can substitute the Level Ancestor query with min, without increasing the complexity for updates and queries. Previously such results have been known only for special cases (e.g. R. E. Tarjan. Applications of path compression on balanced trees. J. ACM, 26(4):690-715, 1979).