On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
A data structure for dynamic trees
Journal of Computer and System Sciences
Implicit representation of graphs
SIAM Journal on Discrete Mathematics
Local management of a global resource in a communication network
Journal of the ACM (JACM)
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
Computer Networks
Small Induced-Universal Graphs and Compact Implicit Graph Representations
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
A Space Lower Bound for Routing in Trees
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Labeling Schemes for Dynamic Tree Networks
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Approximate Distance Labeling Schemes
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
SIAM Journal on Computing
Compact Labeling Scheme for Ancestor Queries
SIAM Journal on Computing
Informative labeling schemes for graphs
Theoretical Computer Science - Mathematical foundations of computer science 2000
Controller and estimator for dynamic networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Upper and lower bounds for routing schemes in dynamic networks
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Computer Networks ISE: A Systems Approach
Computer Networks ISE: A Systems Approach
Labeling schemes for weighted dynamic trees
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
General compact labeling schemes for dynamic trees
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Labeling schemes for vertex connectivity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Improved compact routing schemes for dynamic trees
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Distributed relationship schemes for trees
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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This paper presents an efficient scheme maintaining a separator decomposition representation in dynamic trees using asymptotically optimal labels. In order to maintain the short labels, the scheme uses relatively low message complexity. In particular, if the initial dynamic tree contains just the root, then the scheme incurs an O(log3 n) amortized message complexity per topology change, where n is the current number of nodes in the tree. As a separator decomposition is a fundamental decomposition of trees used extensively as a component in many static graph algorithms, our dynamic scheme for separator decomposition may be used for constructing dynamic versions to these algorithms. The paper then shows how to use our dynamic separator decomposition to construct rather efficient labeling schemes on dynamic trees, using the same message complexity as our dynamic separator scheme. Specifically, we construct efficient routing schemes on dynamic trees, for both the designer and the adversary port models, which maintain optimal labels, up to a multiplicative factor of O(log log n). In addition, it is shown how to use our dynamic separator decomposition scheme to construct dynamic labeling schemes supporting the ancestry and NCA relations using asymptotically optimal labels, as well as to extend a known result on dynamic distance labeling schemes.