A data structure for dynamic trees
Journal of Computer and System Sciences
Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Local management of a global resource in a communication network
Journal of the ACM (JACM)
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Compact labeling schemes for ancestor queries
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Labeling schemes for flow and connectivity
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Reachability and distance queries via 2-hop labels
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved labeling scheme for ancestor queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A comparison of labeling schemes for ancestor queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Labeling schemes for small distances in trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Informative Labeling Schemes for Graphs
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Maintaining Center and Median in Dynamic Trees
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Short and Simple Labels for Small Distances and Other Functions
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Distance Labeling Schemes for Well-Separated Graph Classes
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
A Space Lower Bound for Routing in Trees
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Proximity-Preserving Labeling Schemes and Their Applications
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Approximate Distance Labeling Schemes
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Labeling schemes for weighted dynamic trees
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Labeling schemes for weighted dynamic trees
Information and Computation
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Dynamic routing schemes for general graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Constructing labeling schemes through universal matrices
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Compact separator decompositions in dynamic trees and applications to labeling schemes
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Labeling schemes for vertex connectivity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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An F- labeling scheme is composed of a marker algorithm for labeling the vertices of a graph with short labels, coupled with a decoder algorithm allowing one to compute F(u,v) of any two vertices u and v directly from their labels. As applications for labeling schemes concern mainly large and dynamically changing networks, it is of interest to study distributed dynamic labeling schemes. A general method for constructing labeling schemes for dynamic trees was previously developed in [28]. This method is based on extending an existing static tree labeling scheme to the dynamic setting. This approach fits many natural functions on trees, such as distance, routing, nearest common ancestor etc.. The resulted dynamic schemes incur overheads (over the static scheme) on the label size and on the communication complexity. In particular, all their schemes yield a multiplicative overhead factor of Ω(log n) on the label sizes of the static schemes. Following [28], we develop a different general method for extending static labeling schemes to the dynamic tree settings. Our method fits the same class of tree functions. In contrast to the above paper, our trade-off is designed to minimize the label size on expense of communication. Informally, for any k we present a dynamic labeling scheme incurring multiplicative overhead factors (over the static scheme) of O(logkn) on the label size and O(klogkn) on the amortized message complexity. In particular, by setting $k = \sqrt{n}$, we obtain dynamic labeling schemes with asymptotically optimal label sizes and sublinear amortized message complexity for the routing and the nearest common ancestor functions.