Implicit representation of graphs
SIAM Journal on Discrete Mathematics
WWW '99 Proceedings of the eighth international conference on World Wide Web
Data on the Web: from relations to semistructured data and XML
Data on the Web: from relations to semistructured data and XML
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
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
Small Induced-Universal Graphs and Compact Implicit Graph Representations
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Informative Labeling Schemes for Graphs
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
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,
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
Labeling Schemes for Flow and Connectivity
SIAM Journal on Computing
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Compact Labeling Scheme for Ancestor Queries
SIAM Journal on Computing
ACM SIGIR Forum
Labeling schemes for weighted dynamic trees
Information and Computation
Improved compact routing schemes for dynamic trees
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Labeling schemes for vertex connectivity
ACM Transactions on Algorithms (TALG)
Distributed relationship schemes for trees
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
An Optimal Labeling for Node Connectivity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
An optimal ancestry scheme and small universal posets
Proceedings of the forty-second ACM symposium on Theory of computing
Labeling recursive workflow executions on-the-fly
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
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An ancestry labeling scheme labels the nodes of any tree in such a way that ancestry queries between any two nodes can be answered just by looking at their corresponding labels. The common measure to evaluate the quality of an ancestry scheme is by its label size, that is the maximum number of bits stored in a label, taken over all n-node trees. The design of ancestry labeling schemes finds applications in XML search engines. In these contexts, even small improvements in the label size are important. As a result, following the proposal of a simple interval based ancestry scheme with label size 2 log n bits (Kannan et al., STOC 88), a considerable amount of work was devoted to improve the bound on the label size. The current state of the art upper bound is log n + O(√log n) bits (Abiteboul et al., SICOMP 06) which is still far from the known log n + Ω(log log n) lower bound (Alstrup et al., SODA 03). Motivated by the fact that typical XML trees have extremely small depth, this paper parameterizes the quality measure of an ancestry scheme not only by the number of nodes in the given tree but also by its depth. Our main result is the construction of an ancestry scheme that labels n-node trees of depth d with labels of size log n + 2 log d + O(1). In addition to our main result, we prove a result that may be of independent interest concerning the existence of a small universal graph for the family of trees with bounded depth.