General compact labeling schemes for dynamic trees
@article{Korman2005GeneralCL, title={General compact labeling schemes for dynamic trees}, author={Amos Korman}, journal={Distributed Computing}, year={2005}, volume={20}, pages={179-193}, url={https://api.semanticscholar.org/CorpusID:5636993} }
This paper investigates labeling schemes for dynamic trees with asymptotically optimal label sizes and sublinear amortized message complexity for the ancestry relation, the id-based and label-based nearest common ancestor relation and the routing function.
Topics
Static Labeling Schemes (opens in a new tab)Dynamic Labeling Schemes (opens in a new tab)Labeling Schemes (opens in a new tab)Dynamic Trees (opens in a new tab)Vertices (opens in a new tab)Amortized Message Complexity (opens in a new tab)Nearest Common Ancestors (opens in a new tab)Communication Complexity (opens in a new tab)Adversary (opens in a new tab)Graphs (opens in a new tab)
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53 References
Labeling Schemes for Dynamic Tree Networks
- 2003
Computer Science, Mathematics
The problem on dynamic trees is considered, efficient distributed schemes for it are proposed, and a more general labeling scheme is introduced for the dynamic tree model, based on extending an existing static tree labeling scheme to the dynamic setting.
Informative labeling schemes for graphs
- 2005
Computer Science, Mathematics
Proximity-Preserving Labeling Schemes and Their Applications
- 1999
Computer Science, Mathematics
It is shown that for the class of n-vertex weighted trees with M-bit edge weights, there exists such a proximity-preserving labeling scheme using O(M log n + log2n) bit labels, and proposed a labeling scheme that can provide approximate estimates to the distance.
Compact labeling schemes for ancestor queries
- 2001
Computer Science
This paper proposes a labeling scheme with maximum label size close to 3/2 log n, which is close to the lower bound of log n that follows from the fact that different vertices must have different labels.
A data structure for dynamic trees
- 1981
Computer Science
An O(mn log n)-time algorithm is obtained to find a maximum flow in a network of n vertices and m edges, beating by a factor of log n the fastest algorithm previously known for sparse graphs.
Improved labeling scheme for ancestor queries
- 2002
Computer Science
A labeling scheme for rooted trees that supports ancestor queries and assigns to each node a label which is a binary string, among other things motivated in connection with efficient representation of information for XML-based search engines for the internet.
Approximate Distance Labeling Schemes
- 2001
Mathematics, Computer Science
This work develops constant approximate distance labeling schemes for the classes of trees, bounded treewidth graphs, planar graphs, k-chordal graphs, and graphs with a dominating pair (including for instance interval, permutation, and AT-free graphs).
Distance labeling schemes for well-separated graph classes
- 2000
Computer Science, Mathematics