Self-adjusting binary search trees
Journal of the ACM (JACM)
A data structure for dynamic trees
Journal of Computer and System Sciences
Use of dynamic trees in a network simplex algorithm for the maximum flow problem
Mathematical Programming: Series A and B
On-line maintenance of the four-components of a graph (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Dynamic expression trees and their applications
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Alpha-algorithms for incremental planarity testing (preliminary version)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Dynamic and static algorithms for optimal placement of resources in a tree
Theoretical Computer Science
Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and k Smallest Spanning Trees
SIAM Journal on Computing
A data structure for dynamically maintaining rooted trees
Journal of Algorithms
Dynamic trees as search trees via Euler tours, applied to the network simplex algorithm
Mathematical Programming: Series A and B
Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
Isomorphism testing and display of symmetries in dynamic trees
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Reductions among high dimensional proximity problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Unique maximum matching algorithms
Journal of Algorithms
Maintaining Minimum Spanning Forests in Dynamic Graphs
SIAM Journal on Computing
On-Line Graph Algorithms with SPQR-Trees
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Maintaining Biconnected Components of Dynamic Planar Graphs
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Maintenance of Triconnected Components of Graphs (Extended Abstract)
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Minimizing Diameters of Dynamic Trees
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Maintaining Tree Projections in Amortized $O$(log $n$) Time.
Maintaining Tree Projections in Amortized $O$(log $n$) Time.
Dynamizing static algorithms, with applications to dynamic trees and history independence
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A subset spanner for Planar graphs,: with application to subset TSP
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Finding the conditional location of a median path on a tree
Information and Computation
An O(n log n) algorithm for maximum st-flow in a directed planar graph
Journal of the ACM (JACM)
Journal of Experimental Algorithmics (JEA)
An experimental analysis of self-adjusting computation
ACM Transactions on Programming Languages and Systems (TOPLAS)
Maintaining dynamic minimum spanning trees: An experimental study
Discrete Applied Mathematics
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Maximum flows and parametric shortest paths in planar graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Data structures for mergeable trees
ACM Transactions on Algorithms (TALG)
Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Multiple-source single-sink maximum flow in directed planar graphs in O(diameter ċ n log n) time
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Shortest path based planar graph cuts for bi-layer segmentation of binocular stereo video
ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume part II
A deterministic o(m log m) time algorithm for the reeb graph
Proceedings of the twenty-eighth annual symposium on Computational geometry
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
Tree compression with top trees
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Sublinear-Time maintenance of breadth-first spanning tree in partially dynamic networks
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We design top trees as a new simpler interface for data structures maintaining information in a fully dynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we show how to maintain the diameter, center, and median of each tree in the forest. The forest can be updated by insertion and deletion of edges and by changes to vertex and edge weights. Each update is supported in O(log n) time, where n is the size of the tree(s) involved in the update. Also, we show how to support nearest common ancestor queries and level ancestor queries with respect to arbitrary roots in O(log n) time. Finally, with marked and unmarked vertices, we show how to compute distances to a nearest marked vertex. The latter has applications to approximate nearest marked vertex in general graphs, and thereby to static optimization problems over shortest path metrics.Technically speaking, top trees are easily implemented either with Frederickson's [1997a] topology trees or with Sleator and Tarjan's [1983] dynamic trees. However, we claim that the interface is simpler for many applications, and indeed our new bounds are quadratic improvements over previous bounds where they exist.