Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Data structures and network algorithms
Data structures and network algorithms
Self-adjusting binary search trees
Journal of the ACM (JACM)
Two algorithms for maintaining order in a list
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
An O (n log log n)-time algorithm for triangulating a simple polygon
SIAM Journal on Computing
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
Bounded ordered dictionaries in O(loglogN) time and O(n) space
Information Processing Letters
A constant update time finger search tree
Information Processing Letters
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Optimal pointer algorithm for finding nearest common ancestors in dynamic trees
Journal of Algorithms
Meldable heaps and boolean union-find
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SIAM Journal on Computing
On the Dynamic Finger Conjecture for Splay Trees. Part I: Splay Sorting log n-Block Sequences
SIAM Journal on Computing
On the Dynamic Finger Conjecture for Splay Trees. Part II: The Proof
SIAM Journal on Computing
Optimal finger search trees in the pointer machine
Journal of Computer and System Sciences - STOC 2002
Dynamizing static algorithms, with applications to dynamic trees and history independence
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Extreme elevation on a 2-manifold
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Lower bounds for dynamic connectivity
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Path Minima in Incremental Unrooted Trees
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Computing Elevation Maxima by Searching the Gauss Sphere
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
A randomized O(m log m) time algorithm for computing Reeb graphs of arbitrary simplicial complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Data structures for mergeable trees
ACM Transactions on Algorithms (TALG)
Computing elevation maxima by searching the gauss sphere
Journal of Experimental Algorithmics (JEA)
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Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant allows an operation that merges two tree paths. In contrast to the standard problem, in which only one tree arc at a time changes, a single merge operation can change many arcs. In spite of this, we develop a data structure that supports merges and all other standard tree operations in O(log2 n) amortized time on an n-node forest. For the special case that occurs in the motivating application, in which arbitrary arc deletions are not allowed, we give a data structure with an O(log n) amortized time bound per operation, which is asymptotically optimal. The analysis of both algorithms is not straightforward and requires ideas not previously used in the study of dynamic trees. We explore the design space of algorithms for the problem and also consider lower bounds for it.